User Manual

Kernels

Kernels are related to the physics involved in the particular analysis. This document focusses on kernel commands related to the geotechnical earthquake engineering applications. Further information can be found in Kernels System.

The main kernel that is used for quasi-static and dynamic analyses is Solid Mechanics Module. This kernel is used to solve the equation of motion without the inertial effects. It requires information about the unknowns that are solved for. The following chunk of commands can be used to activate dynamic tensor mechanics kernel along with Newmark-beta integration scheme, inertial effects, and two mode Rayleigh viscous damping (both stiffness and mass proportional damping):

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./DynamicTensorMechanics<<<{"href": "../../syntax/Kernels/DynamicTensorMechanics/index.html"}>>>]
    displacements<<<{"description": "The nonlinear displacement variables for the problem"}>>> = 'disp_x disp_y disp_z'
    stiffness_damping_coefficient<<<{"description": "Name of material property or a constant real number defining stiffness Rayleigh parameter (zeta)."}>>> = 0.00006366
  [../]
  [./inertia_x]
    type = InertialForce<<<{"description": "Calculates the residual for the inertial force ($M \\cdot acceleration$) and the contribution of mass dependent Rayleigh damping and HHT time  integration scheme ($\\eta \\cdot M \\cdot ((1+\\alpha)velq2-\\alpha \\cdot vel-old) $)", "href": "../../source/kernels/InertialForce.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    eta<<<{"description": "Name of material property or a constant real number defining the eta parameter for the Rayleigh damping."}>>> = 7.854
  [../]
  [./inertia_y]
    type = InertialForce<<<{"description": "Calculates the residual for the inertial force ($M \\cdot acceleration$) and the contribution of mass dependent Rayleigh damping and HHT time  integration scheme ($\\eta \\cdot M \\cdot ((1+\\alpha)velq2-\\alpha \\cdot vel-old) $)", "href": "../../source/kernels/InertialForce.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    eta<<<{"description": "Name of material property or a constant real number defining the eta parameter for the Rayleigh damping."}>>> = 7.854
  [../]
  [./inertia_z]
    type = InertialForce<<<{"description": "Calculates the residual for the inertial force ($M \\cdot acceleration$) and the contribution of mass dependent Rayleigh damping and HHT time  integration scheme ($\\eta \\cdot M \\cdot ((1+\\alpha)velq2-\\alpha \\cdot vel-old) $)", "href": "../../source/kernels/InertialForce.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    eta<<<{"description": "Name of material property or a constant real number defining the eta parameter for the Rayleigh damping."}>>> = 7.854
  [../]
  [./gravity]
    type = Gravity<<<{"description": "Apply gravity. Value is in units of acceleration.", "href": "../../source/kernels/Gravity.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    value<<<{"description": "Value multiplied against the residual, e.g. gravitational acceleration"}>>> = -9.81
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_xy
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 1
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 0
  [../]
  [./stress_yz]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_yz
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 2
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 1
  [../]
  [./stress_zx]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_zx
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 0
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 2
  [../]
  [./strain_xy]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_xy
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 1
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 0
  [../]
  [./strain_yz]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = strain_yz
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 2
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 1
  [../]
  [./strain_zx]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = strain_zx
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 0
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 2
  [../]
  [./stress_xx]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_xx
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 0
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 0
  [../]
  [./stress_yy]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_yy
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 1
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 1
  [../]
  [./stress_zz]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = stress
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = stress_zz
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 2
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 2
  [../]
  [./strain_xx]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = strain_xx
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 0
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 0
  [../]
  [./strain_yy]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> =total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = strain_yy
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 1
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 1
  [../]
  [./strain_zz]
    type = RankTwoAux<<<{"description": "Access a component of a RankTwoTensor", "href": "../../source/auxkernels/RankTwoAux.html"}>>>
    rank_two_tensor<<<{"description": "The rank two material tensor name"}>>> = total_strain
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = strain_zz
    index_i<<<{"description": "The index i of ij for the tensor to output (0, 1, 2)"}>>> = 2
    index_j<<<{"description": "The index j of ij for the tensor to output (0, 1, 2)"}>>> = 2
  [../]
  [./layer]
    type = UniformLayerAuxKernel<<<{"description": "Computes an AuxVariable for representing a layered structure in an arbitrary direction.", "href": "../../source/auxkernels/UniformLayerAuxKernel.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = layer_id
    interfaces<<<{"description": "A list of layer interface locations to apply across the domain in the specified direction."}>>> = '2.0'
    direction<<<{"description": "The direction to apply layering."}>>> = '0 0 1'
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = initial
  [../]
[]

displacements = 'disp_x disp_y disp_z' line is not necessary if the displacements are already defined as global parameters but are provided here for the sake of completeness. Beta and gamma are the parameters of Newmark-beta integration scheme. Zeta and eta are the stiffness and mass matrix coefficients of Rayleigh damping formulation (see Solid Mechanics Module and Theory Manual for more information). Auxiliary kernels are specified to calculate the acceleration and velocities using Newmark-beta scheme at the end of each time step where the displacement is already solved and known. Lastly, stress_xy is defined as an auxiliary variable. This is achieved by specifying the type of the Auxkernel as RankTwoAux. RankTwoAux means that the source of the auxiliary variable is a rank two tensor, and the type of rank two tensor is explicitly defined as stress tensor using the command "rank_two_tensor = stress". Since, the variable is stress_xy, the location in the stress tensor corresponding to stress_xy needs to be specified using index_i (row index) and index_j (column index). To request for stress_xy, index_i is set to 0 and index_j is set to 1. The next section explains the boundary conditions that are required to run a simple, quasi-static and dynamic analyses.

Prescribed Displacement

The preset displacement boundary condition can be used to apply a displacement time history to a boundary (at the nodes). The displacement boundary condition first converts the user defined displacement time history to an acceleration time history using Backward Euler finite difference scheme. This acceleration is then integrated to get displacement using Newmark-beta method. The resulting displacement is then applied as a kinematic displacement boundary condition. The following command can be used to apply the preset displacement boundary condition:

  [./top_x]
    type = PresetDisplacement
    boundary = 5
    variable = disp_x
    beta = 0.25
    velocity = vel_x
    acceleration = accel_x
    function = top_disp
  [../]
[]

The above command should be embedded inside the BCs command block. "boundary = 5" assigns the preset displacement to boundary 5 which, in this case, is a predefined boundary of a single element as described in single element problem above. Alternatively, the boundary number can be identified using Cubit or Trelis. "variable = disp_x" imposes the boundary condition on the x direction. "beta" is the Newmark-beta integration parameter. The "function = top_disp" specifies the function that defines the loading time history. It is defined in the "Functions" block as follows:

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./top_disp]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = Displacement2.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

Displacement2.csv is the file, located in the same directory of the input file, containing the displacement time history. The first column of this file should contain the time vector starting at 0.0. The second column should contain the displacement values. "type = PiecewiseLinear" defines the type of the function which is in this case piecewise-linear. "format" specifies the format of the data file, i.e. whether the data is in columns or rows.

Prescribed Acceleration

The preset acceleration boundary condition can be used to apply an acceleration time history to a boundary. The preset acceleration boundary condition integrates the given acceleration time history to get the displacement using Newmark-beta method. This displacement is then applied as a kinematic displacement boundary condition. Syntax is the same as prescribing a displacement boundary condition but with type = PresetAcceleration and the function describing time vs acceleration data instead of time vs displacement.

Periodic Boundary Conditions

Periodic boundary conditions are used to constrain the nodes to move together in the specified directions. The following input is an example applied on the single element problem above and should be embedded into the BCs block segment as:

  [./Periodic]
    [./x_dir]
      variable = 'disp_x disp_y disp_z'
      primary = '4'
      secondary = '2'
      translation = '1.0 0.0 0.0'
    [../]
    [./y_dir]
      variable = 'disp_x disp_y disp_z'
      primary = '1'
      secondary = '3'
      translation = '0.0 1.0 0.0'
    [../]
  [../]

Linear elastic soil

A linear elastic soil can be defined in MASTODON by defining a elasticity tensor using ComputeIsotropicElasticityTensor, stress calculator using ComputeLinearElasticStress, and a small strain calculator using ComputeSmallStrain. Density can be defined using the GenericConstantMaterial. An example of these input blocks is shown below:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./Elasticity_tensor_1]
    type = ComputeIsotropicElasticityTensor<<<{"description": "Compute a constant isotropic elasticity tensor.", "href": "../../source/materials/ComputeIsotropicElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    youngs_modulus<<<{"description": "Young's modulus of the material."}>>> = 2.e+2
    poissons_ratio<<<{"description": "Poisson's ratio for the material."}>>> = 0.4
  [../]

  [./strain_1]
    type = ComputeSmallStrain<<<{"description": "Compute a small strain.", "href": "../../source/materials/ComputeSmallStrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    displacements<<<{"description": "The displacements appropriate for the simulation geometry and coordinate system"}>>> = 'disp_x disp_y disp_z'
  [../]

  [./stress_1]
    type = ComputeLinearElasticStress<<<{"description": "Compute stress using elasticity for small strains", "href": "../../source/materials/ComputeLinearElasticStress.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
  [../]

  [./density_1]
    type = GenericConstantMaterial<<<{"description": "Declares material properties based on names and values prescribed by input parameters.", "href": "../../source/materials/GenericConstantMaterial.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    prop_names<<<{"description": "The names of the properties this material will have"}>>> = 'density'
    prop_values<<<{"description": "The values associated with the named properties"}>>> = '1.'
  [../]

[]

The I_Soil System

The I-soil material model is a nonlinear hysteretic soil model that is based on the distributed element models developed by Iwan (1967) and Chiang and Beck (1994). In 1-D, this model takes the backbone stress-strain curve and divides it into a set of elastic-perfectly plastic curves. The total stress then is the sum of the stresses from the individual elastic-perfectly plastic curves.

The three dimensional generalization of this model is achieved using von-Mises failure criteria for each elastic-perfectly plastic curve resulting in an invariant yield surfaces in three-dimensional stress space like in Figure 2 (after Chiang and Beck (1994)).

Figure 2: Invariant yield surfaces of the individual elastic-perfectly curves.

The following options are available for an automatic creation of the backbone curve:

1. User-defined backbone curve (soil_type = 'user_defined'): The backbone curve can be provided in a csv file where the first column is shear strain and the second column is shear stress. The number of elastic-perfectly plastic curves that will be generated from this backbone curve depends on the number of entries in the data file. When many soil layers are present, a vector of data files can be provided as input. The size of this vector should equal the number of soil layers. Also the number of entries in each data file should be the same.

2. Darendeli backbone curve (soil_type = 'darendeli'): The backbone curve can be auto-generated based on empirical data for common soil types. Darendeli (2001) presents a functional form that can be used to create the backbone shear stress - strain curves based on the experimental results obtained from resonant column and torsional shear tests. This functional form requires the initial shear modulus, initial bulk modulus, plasticity index, over consolidation ratio, reference mean confining pressure (p_ref) and number of points as input. Other than the number of points, all the other parameters can be provided as a vector for each soil layer. The number of points, which determines the number of elastic-perfectly plastic curves to be generated, is constant for all soil layers.

3. General Quadratic/Hyperbolic (GQ/H) backbone curve (soil_type = 'gqh'): Darendeli (2001) study constructs the shear stress-strain curves based on experimentally obtained data. At small strains the data is obtained using resonant column test, and towards the medium shear strain levels the torsional shear test results are used. The values are extrapolated at the large strain levels. This extrapolation may underestimate or overestimate the shear strength at large strains. Therefore, shear strength correction is necessary to account for the correct shear strength at large strains. GQ/H model proposed by Groholski et al. (2016) has a curve fitting scheme that automatically corrects the reference curves provided by Darendeli (2001) based on the specific shear strength at the large strains. This model requires taumax, theta_1 through 5, initial shear modulus, initial bulk modulus and number of points as input. The parameter taumax is the maximum shear stress that can be generated in the soil. The parameters theta_1 through 5 are the curve fitting parameters and can be obtained using DEEPSOIL (Hashash et al., 2016). Other than the number of points, all the other parameters can be given as a vector for the different soil layers. The number of points, which determines the number of elastic-perfectly plastic curves to be generated, is constant for all soil layers.

4. Thin-layer friction backbone curve (soil_type = 'thin_layer'): This backbone curve is should be used for the simulation of the foundation-soil interfaces using a formulation similar to Coulomb friction. This option should be used for a thin layer of I-soil elements along the foundation-soil interface. Using the 'thin_layer' option creates a bilinear backbone curve with a pre-yield shear modulus equal to the the initial_shear_modulus, and a post-yield shear modulus equal to initial_shear_modulus * hardening_ratio. The shear stress at yield is set to be equal to friction_coefficient * instantaneous pressure. Using the 'thin_layer' option for the I-Soil backbone curve automatically sets the values pressure_dependency = 'true', , and . This ensures that the shear strength dependence is turned on, and the strength of the thin layer increases linearly with instantaneous pressure. Note that since the strength is directly proportional to pressure (and not normal stress), this is not identical to Coulomb formulation.

All the above backbone curves provide the behavior of the soil at a reference confining pressure (). When the confining pressure of the soil changes, the soil behavior also changes (if pressure dependency is turned on). The shear modulus () at a pressure is given by:

where is the initial shear modulus, is the tension pressure cut off and is a parameter obtained from experiments. The shear modulus reduces to zero for any pressure lower than to model the failure of soil in tension. Note that compressive pressure is taken to be positive.

Similarly, the yield stress () of the elastic-perfectly plastic curve also changes when the confining pressure changes. The yield stress () at a pressure is given as:

where , and are parameters obtained from experiments.

To include pressure-dependent stiffness and yield strength calculation, pressure_dependency should be set to true and b_exp, a_0, a_1, a_2, tension_pressure_cut_off and p_ref need to be provided as input. Other than p_ref, all the other parameters are the same for all the soil layers. p_ref can be provided as vector with information about each soil layer.

Lead-Rubber Isolator

The lead-rubber (LR) isolator material should be used with two-noded beam or link type elements in MASTODON. For each subdomain (which may contain multiple link elements), the material properties are defined by creating material blocks, ComputeIsolatorDeformation and ComputeLRIsolatorElasticity, and the kernel block, StressDivergenceIsolator. A sample definition of the kernel and material block is shown in the input file below.

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 3
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 4
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 5
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_zz
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./deformation]
    type = ComputeIsolatorDeformation<<<{"description": "Compute the deformations and rotations in a two-noded isolator element.", "href": "../../source/materials/ComputeIsolatorDeformation.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    sd_ratio<<<{"description": "Shear distance ratio."}>>> = 0.5
    y_orientation<<<{"description": "Orientation of the local Y direction along which, Ky is provided. This should be perpendicular to the axis of the isolator."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables appropriate for the simulation geometry and coordinate system."}>>> = 'rot_x rot_y rot_z'
    velocities<<<{"description": "Translational velocity variables."}>>> = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeLRIsolatorElasticity<<<{"description": "Compute the forces and the stiffness matrix for an LR isolator element.", "href": "../../source/materials/ComputeLRIsolatorElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    fy<<<{"description": "Yield strength of the bearing."}>>> = 207160
    alpha<<<{"description": "Ratio of post-yield shear stiffness to the initial elastic shear stiffness of the bearing. This is dimensionless"}>>> = 0.03812
    G_rubber<<<{"description": "Shear modulus of rubber."}>>> = 0.87e6
    K_rubber<<<{"description": "Bulk modulus of rubber."}>>> = 2e9
    D1<<<{"description": "Diameter of lead core."}>>> = 0.1397
    D2<<<{"description": "Outer diameter of the bearing."}>>> = 0.508
    ts<<<{"description": "Thickness of a single steel shim."}>>> = 0.00476
    tr<<<{"description": "Thickness of a single rubber layer."}>>> = 0.009525
    n<<<{"description": "Number of rubber layers."}>>> = 16
    tc<<<{"description": "Thickness of the rubber cover of the bearing."}>>> = 0.0127
    kc<<<{"description": "Cavitation parameter."}>>> = 20
    phi_m<<<{"description": "Damage index."}>>> = 0.75
    ac<<<{"description": "Strength degradation parameter."}>>> = 1
    cd<<<{"description": "Viscous damping parameter."}>>> = 0
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
    k_steel<<<{"description": "Thermal conductivity of steel. Defaults to 50.0 W/(m-oC)."}>>> = 50
    a_steel<<<{"description": "Thermal diffusivity of steel. Defaults to 1.41e-05 m2/s."}>>> = 1.41e-5
    rho_lead<<<{"description": "Density of lead. Defaults to 11200 kg/m3."}>>> = 11200
    c_lead<<<{"description": "Specific heat capacity of lead. Defaults to 130.0 N-m/kg oC."}>>> = 130
    cavitation<<<{"description": "Switch for modeling cavitation and post-cavitation."}>>> = true
    horizontal_stiffness_variation<<<{"description": "Switch for modeling variation of horizontal stiffness during the analysis."}>>> = true
    vertical_stiffness_variation<<<{"description": "Switch for modeling variation of vertical stiffness during the analysis."}>>> = true
    strength_degradation<<<{"description": "Switch for modeling strength degradation due to lead core heating."}>>> = true
    buckling_load_variation<<<{"description": "Switch for modeling buckling load variation during the analysis."}>>> = true
  [../]
[]

A description of each of the input parameters is provided in the syntax description below. Additionally, the behavior of the LR isolator element in the axial and shear directions is demonstrated using the three examples described below. Analysis results are compared with verified and validated numerical models implemented in the commercial software code, ABAQUS Dassault Systòmes (2018).

Example 1: Response to axial loading

The input file below demonstrates the response of the LR isolator element in the axial direction. A cyclic displacement is applied at the top node of the isolator in the axial (local X) direction while the bottom node is restrained in all six degrees of freedom. To simulate the coupled (shear and axial) response, a ramped displacement is applied at the top node in the shear (local Y) direction.

# Test for lead rubber isolator in Axial (compression and tension)

#Loading conditions

# i)  A ramp displacement in shear(y_direction)
# ii) A cyclic displacement loading in axial (x_direction)

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
  displacements<<<{"description": "The variables corresponding to the x y z displacements of the mesh.  If this is provided then the displacements will be taken into account during the computation. Creation of the displaced mesh can be suppressed even if this is set by setting 'use_displaced_mesh = false'."}>>> = 'disp_x disp_y disp_z'
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./disp_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixy0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./disp_x_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    function<<<{"description": "Function describing the displacement."}>>> = history_disp_axial
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = accel_x
    velocity<<<{"description": "The velocity variable."}>>> = vel_x
  [../]
  [./disp_y_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    function<<<{"description": "Function describing the displacement."}>>> = history_disp_shear
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = accel_y
    velocity<<<{"description": "The velocity variable."}>>> = vel_y
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./history_disp_axial]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = disp_axial_ct.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
  [./history_disp_shear]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>> = '0.0 10.0'
    y<<<{"description": "The ordinate values"}>>> = '0.0 0.3048'
    [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = -0.02
  end_time = 2.5
  dt = 0.005
  dtmin = 0.001
  timestep_tolerance = 1e-6
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 3
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 4
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 5
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_zz
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./deformation]
    type = ComputeIsolatorDeformation<<<{"description": "Compute the deformations and rotations in a two-noded isolator element.", "href": "../../source/materials/ComputeIsolatorDeformation.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    sd_ratio<<<{"description": "Shear distance ratio."}>>> = 0.5
    y_orientation<<<{"description": "Orientation of the local Y direction along which, Ky is provided. This should be perpendicular to the axis of the isolator."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables appropriate for the simulation geometry and coordinate system."}>>> = 'rot_x rot_y rot_z'
    velocities<<<{"description": "Translational velocity variables."}>>> = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeLRIsolatorElasticity<<<{"description": "Compute the forces and the stiffness matrix for an LR isolator element.", "href": "../../source/materials/ComputeLRIsolatorElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    fy<<<{"description": "Yield strength of the bearing."}>>> = 207160
    alpha<<<{"description": "Ratio of post-yield shear stiffness to the initial elastic shear stiffness of the bearing. This is dimensionless"}>>> = 0.03812
    G_rubber<<<{"description": "Shear modulus of rubber."}>>> = 0.87e6
    K_rubber<<<{"description": "Bulk modulus of rubber."}>>> = 2e9
    D1<<<{"description": "Diameter of lead core."}>>> = 0.1397
    D2<<<{"description": "Outer diameter of the bearing."}>>> = 0.508
    ts<<<{"description": "Thickness of a single steel shim."}>>> = 0.00476
    tr<<<{"description": "Thickness of a single rubber layer."}>>> = 0.009525
    n<<<{"description": "Number of rubber layers."}>>> = 16
    tc<<<{"description": "Thickness of the rubber cover of the bearing."}>>> = 0.0127
    kc<<<{"description": "Cavitation parameter."}>>> = 20
    phi_m<<<{"description": "Damage index."}>>> = 0.75
    ac<<<{"description": "Strength degradation parameter."}>>> = 1
    cd<<<{"description": "Viscous damping parameter."}>>> = 0
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
    k_steel<<<{"description": "Thermal conductivity of steel. Defaults to 50.0 W/(m-oC)."}>>> = 50
    a_steel<<<{"description": "Thermal diffusivity of steel. Defaults to 1.41e-05 m2/s."}>>> = 1.41e-5
    rho_lead<<<{"description": "Density of lead. Defaults to 11200 kg/m3."}>>> = 11200
    c_lead<<<{"description": "Specific heat capacity of lead. Defaults to 130.0 N-m/kg oC."}>>> = 130
    cavitation<<<{"description": "Switch for modeling cavitation and post-cavitation."}>>> = true
    horizontal_stiffness_variation<<<{"description": "Switch for modeling variation of horizontal stiffness during the analysis."}>>> = true
    vertical_stiffness_variation<<<{"description": "Switch for modeling variation of vertical stiffness during the analysis."}>>> = true
    strength_degradation<<<{"description": "Switch for modeling strength degradation due to lead core heating."}>>> = true
    buckling_load_variation<<<{"description": "Switch for modeling buckling load variation during the analysis."}>>> = true
  [../]
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./disp_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_x
  [../]
  [./vel_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_x
  [../]
  [./accel_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_x
  [../]
  [./reaction_x]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./disp_y]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_y
  [../]
  [./vel_y]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_y
  [../]
  [./accel_y]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_y
  [../]
  [./reaction_y]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_y
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./disp_z]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_z
  [../]
  [./vel_z]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_z
  [../]
  [./accel_z]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_z
  [../]
  [./reaction_z]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_z
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./reaction_xx]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_xx
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./reaction_yy]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_yy
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./reaction_zz]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_zz
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
[]

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
[]

(test/tests/materials/lr_isolator/lr_isolator_axial_ct.i)

The response of the LR isolator to cyclic loading in the axial direction is shown in Figure 3.

Figure 3: Axial response of the LR isolator to the prescribed cyclic loading.

Example 2: Response to shear loading

The input file below simulates the response of the LR isolator element in the shear direction. A sinusoidal displacement is applied at the top node of the isolator in the shear (local Y) direction. The isolator element has the same set of constraints as in Example 1. A constant axial load is applied to the isolator in the axial direction to simulate the weight of the superstructure.

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixy0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [fixz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [fixrx1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./disp_y_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    function<<<{"description": "Function describing the displacement."}>>> = history_shear_dispy
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_y'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_y'
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./force_x]
    type = UserForcingFunctionNodalKernel<<<{"description": "Residual contribution to an ODE from a source function acting at nodes.", "href": "../../source/nodalkernels/UserForcingFunctionNodalKernel.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'right'
    function<<<{"description": "The forcing function"}>>> = force_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./force_x]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>> = '0.0 1.0  11.0'
    y<<<{"description": "The ordinate values"}>>> = '0.0 -1439520 -1439520'
  [../]
  [./history_shear_dispy]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = disp_shear.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

(test/tests/materials/lr_isolator/lr_isolator_shear.i)

The response of the LR isolator to cyclic loading in the shear direction is shown in Figure 4.

Figure 4: Shear response of the LR isolator to the prescribed cyclic loading.

Example 3: Response to seismic loading

The input file below simulates the response of the LR isolator to seismic loading. A superstructure mass of 146890 kg is assumed in this example, and is assigned to the top node of the isolator using a NodalKernel of type, NodalTranslationInertia. Three components of ground motion are applied at the bottom node as input accelerations, using the PresetAcceleration BC. A small time step in the range of 0.0005-0.0001 sec is required for seismic analysis, especially for accuracy in the axial direction. It is recommended to iteratively reduce the time step till the change in the results is within a desired tolerance.

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
[./fixx0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixy0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixz0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixrx0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixry0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixrz0]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixrx1]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixry1]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./fixrz1]
  type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
  boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
  value<<<{"description": "Value of the BC"}>>> = 0.0
[../]
[./accel_x0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_x
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_x'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_x'
[../]
[./accel_y0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_y
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_y'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_y'
[../]
[./accel_z0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_z
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_z'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_z'
[../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
[./x_inertial1]
  type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
  velocity<<<{"description": "velocity variable"}>>> = vel_x
  acceleration<<<{"description": "acceleration variable"}>>> = accel_x
  boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
  beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
  gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
  mass<<<{"description": "Mass associated with the node"}>>> = 146890
  alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
  eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
[../]
[./y_inertial1]
  type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
  velocity<<<{"description": "velocity variable"}>>> = vel_y
  acceleration<<<{"description": "acceleration variable"}>>> = accel_y
  boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
  beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
  gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
  mass<<<{"description": "Mass associated with the node"}>>> = 146890
  alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
  eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
[../]
[./z_inertial1]
  type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
  velocity<<<{"description": "velocity variable"}>>> = vel_z
  acceleration<<<{"description": "acceleration variable"}>>> = accel_z
  boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
  beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
  gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
  mass<<<{"description": "Mass associated with the node"}>>> = 146890
  alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
  eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
[../]

[./force_x]
  type = UserForcingFunctionNodalKernel<<<{"description": "Residual contribution to an ODE from a source function acting at nodes.", "href": "../../source/nodalkernels/UserForcingFunctionNodalKernel.html"}>>>
  variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
  boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'right'
  function<<<{"description": "The forcing function"}>>> = force_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
[./acceleration_x]
  type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
  data_file<<<{"description": "File holding CSV data"}>>> = accel_x.csv
  format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
[../]
[./acceleration_y]
  type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
  data_file<<<{"description": "File holding CSV data"}>>> = accel_y.csv
  format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
[../]
[./acceleration_z]
  type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
  data_file<<<{"description": "File holding CSV data"}>>> = accel_z.csv
  format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
[../]
[./force_x]
  type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
  x<<<{"description": "The abscissa values"}>>>='0.0 0.05 50'
  y<<<{"description": "The ordinate values"}>>>='0.0 -1468900 -1468900'
  [../]
[]

(test/tests/materials/lr_isolator/lr_isolator_seismic.i)

The figures below show the response of the LR isolator to the prescribed seismic loading.

Figure 5: Axial response of the LR isolator to the prescribed seismic loading.

Figure 6: Response of the LR isolator in the shear (local y) direction to the prescribed seismic loading.

Figure 7: Response of the LR isolator in the shear (local z) direction to the prescribed seismic loading.

Friction Pendulum^TM Isolator

ComputeFPIsolatorElasticity material simulates the behavior of a single concave Friction Pendulum^TM bearing in MASTODON, and is used with a two-noded link type element. The material properties are defined by creating material blocks: ComputeIsolatorDeformation and ComputeFPIsolatorElasticity, and the kernel block, StressDivergenceIsolator. A description of each of the input parameters is provided here. To model the co-efficient of sliding friction as a function of the axial pressure, sliding velocity, and the instantaneous temperature, the following switch parameters are used:

pressure_dependent = true, velocity_dependent = true, and temperature_change = true.

The axial and rotational terms of the basic stiffness matrix of the bearing element can be specified using the optional parameters: k_x, k_xx, k_yy, k_zz. A default value of 10e13 is assumed when SI units are used. The stiffness value should be sufficiently high to simulate rigid behavior in these degrees of freedom. In the pressure factor computation kp, the instantaneous pressure and reference pressure values are in MPa. The user is required to provide information on the current unit system used in the material parameter unit, so that corresponding conversion factors are computed.

unit = 1.0 for N-m-s; unit = 2.0 for kN-m-s); unit = 3.0 for N-mm-s; unit = 4.0 for kN-mm-s; unit = 5.0 for lb-in-s; unit = 6.0 for kip-in-s; unit = 7.0 for lb-ft-s; unit = 8.0 for kip-ft-s;

The behavior of the FP bearing element in the shear direction is demonstrated using the examples described below. Analysis results are compared with verified and validated numerical models implemented in the open-source finite element package OpenSees (Mazzoni et al., 2009).

Example: Response to cyclic loading in shear

The input file below demonstrates the response of the FP bearing subjected to cyclic loading in the shear direction. Three test cases: where co-efficient of friction as a function of the axial pressure only, co-efficient of friction as a function of the sliding velocity only, and coefficient of friction as a function of the instantaneous temperature only, are defined. A sinusoidal displacement history of Figure 8 is applied to the top node and the bottom node is restrained in the six degrees-of-freedom for all the three test cases. A constant axial load of 6285710 N is applied to the top node to simulate the weight of the superstructure.

# Test for Friction Pendulum isolator in shear

#Loading conditions

# i)  A constant axial load acting on isolator
# ii) A sinusoidal displacement in shear (y_direction)

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  displacements<<<{"description": "The variables corresponding to the x y z displacements of the mesh.  If this is provided then the displacements will be taken into account during the computation. Creation of the displaced mesh can be suppressed even if this is set by setting 'use_displaced_mesh = false'."}>>> = 'disp_x disp_y disp_z'
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./disp_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 3
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 4
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 5
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_zz
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_x
    displacement<<<{"description": "displacement variable"}>>> = rot_x
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_y
    displacement<<<{"description": "displacement variable"}>>> = rot_y
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_z
    displacement<<<{"description": "displacement variable"}>>> = rot_z
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixy0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./disp_y_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    function<<<{"description": "Function describing the displacement."}>>> = history_shear_dispy
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_y'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_y'
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./force_x]
    type = UserForcingFunctionNodalKernel<<<{"description": "Residual contribution to an ODE from a source function acting at nodes.", "href": "../../source/nodalkernels/UserForcingFunctionNodalKernel.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'right'
    function<<<{"description": "The forcing function"}>>> = force_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./force_x]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>> = '0.0 1.0  11.0'
    y<<<{"description": "The ordinate values"}>>> = '0.0 -6285710 -6285710'
  [../]
  [./history_shear_dispy]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = disp_shear.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = 0
  end_time = 2.5
  dt = 0.005
  dtmin = 0.0001
  timestep_tolerance = 1e-6
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./deformation]
    type = ComputeIsolatorDeformation<<<{"description": "Compute the deformations and rotations in a two-noded isolator element.", "href": "../../source/materials/ComputeIsolatorDeformation.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    sd_ratio<<<{"description": "Shear distance ratio."}>>> = 0.5
    y_orientation<<<{"description": "Orientation of the local Y direction along which, Ky is provided. This should be perpendicular to the axis of the isolator."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables appropriate for the simulation geometry and coordinate system."}>>> = 'rot_x rot_y rot_z'
    velocities<<<{"description": "Translational velocity variables."}>>> = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeFPIsolatorElasticity<<<{"description": "Compute the forces and the stiffness matrix for a single concave Friction Pendulum isolator element.", "href": "../../source/materials/ComputeFPIsolatorElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    mu_ref<<<{"description": "Reference co-efficient of friction."}>>> = 0.06
    p_ref<<<{"description": "Reference axial pressure."}>>> = 50e6
    diffusivity<<<{"description": "Thermal diffusivity of steel."}>>> = 4.4e-6
    conductivity<<<{"description": "Thermal conductivity of steel."}>>> = 18
    a<<<{"description": "Rate parameter."}>>> = 100
    r_eff<<<{"description": "Effective radius of curvature of sliding surface."}>>> = 2.2352
    r_contact<<<{"description": "Radius of contact area at sliding surface."}>>> = 0.2
    uy<<<{"description": "Yield displacement of the bearing in shear."}>>> = 0.001
    unit<<<{"description": "Tag for conversion in the pressure factor computation when different unit systems are used. Enter 1 for N m s C;  2 for kN m s C;  3 for N mm s C;  4 for kN mm s C;  5 for lb in s C;  6 for kip in s C;  7 for lb ft s C;  8 for kip ft s C. "}>>> = 1
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
    pressure_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous pressure."}>>> = true
    temperature_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous temperature."}>>> = true
    velocity_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous sliding velocity."}>>> = true
  [../]
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./disp_y]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_y
  [../]
  [./reaction_y]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = 'reaction_y'
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'left'
  [../]
[]

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
[]

(test/tests/materials/fp_isolator/fp_isolator_shear_PTV.i)

Figure 8: Displacement loading history along the shear direction of the bearing.

The response of the FP bearing to cyclic loading in the shear direction is shown in Figure 9

Figure 9: Response of the FP bearing to the prescribed cyclic loading in shear.

Example: Response to seismic loading

The input file below describes the response of the FP bearing to seismic excitation. A superstructure mass of 640745 kg is assumed for the purpose of this example, and is assigned to the top node of the bearing using a NodalKernel of type, NodalTranslationInertia. Three components of ground motion are applied at the bottom node as input accelerations, using the PresetAcceleration BC. An axial load is applied on the bearing to account for the weight of superstructure. For the initial few time steps, where gravity load is being applied, inertia objects are disabled using control block to avoid any dynamic effects.

# Test for Friction Pendulum isolator under seismic loading

# coefficient of friction depends on velocity, pressure and temperature

#Loading conditions

# i) Seismic loading(ground motion) as acceleration profile at bottom node in 3 directions

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  xmin = 0
  xmax = 0.224
  nx =  1
  dim = 1
  displacements<<<{"description": "The variables corresponding to the x y z displacements of the mesh.  If this is provided then the displacements will be taken into account during the computation. Creation of the displaced mesh can be suppressed even if this is set by setting 'use_displaced_mesh = false'."}>>> = 'disp_x disp_y disp_z'
[]

[Controls<<<{"href": "../../syntax/Controls/index.html"}>>>]
  [./C1]
    type = TimePeriod<<<{"description": "Control the enabled/disabled state of objects with time.", "href": "../../source/controls/TimePeriod.html"}>>>
    disable_objects<<<{"description": "A list of object tags to disable."}>>> = '*::x_inertial1 *::y_inertial1 *::z_inertial1 *::vel_x *::vel_y *::vel_z *::accel_x *::accel_y *::accel_z'
    start_time<<<{"description": "The time at which the objects are to be enabled/disabled."}>>> = '0'
    end_time<<<{"description": "The time at which the objects are to be enable/disabled."}>>> = '0.10'
  [../]
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./disp_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 3
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 4
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator<<<{"description": "Kernel for isolator element", "href": "../../source/kernels/StressDivergenceIsolator.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for isolator."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables for the isolator."}>>> = 'rot_x rot_y rot_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z, 3 for rot_x, 4 for rot_y and 5 for rot_z)."}>>> = 5
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_zz
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_x
    displacement<<<{"description": "displacement variable"}>>> = rot_x
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_y
    displacement<<<{"description": "displacement variable"}>>> = rot_y
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_accel_z
    displacement<<<{"description": "displacement variable"}>>> = rot_z
    velocity<<<{"description": "velocity variable"}>>> = rot_vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./rot_vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = rot_vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = rot_accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixrx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrx1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixry1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./accel_x0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_x
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_x'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_x'
  [../]
  [./accel_y0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_y
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_y'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_y'
  [../]
  [./accel_z0]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_z
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_z'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_z'
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./x_inertial1]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 640745
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
  [../]
  [./y_inertial1]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 640745
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
  [../]
  [./z_inertial1]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 640745
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> =0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> =0
  [../]
  [./force_x]
    type = UserForcingFunctionNodalKernel<<<{"description": "Residual contribution to an ODE from a source function acting at nodes.", "href": "../../source/nodalkernels/UserForcingFunctionNodalKernel.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'right'
    function<<<{"description": "The forcing function"}>>> = force_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./acceleration_x]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = accel_x.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
  [../]
  [./acceleration_y]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = accel_y.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
  [../]
  [./acceleration_z]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = accel_z.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>>=columns
  [../]
  [./force_x]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>>='0.0 0.05 50.11'
    y<<<{"description": "The ordinate values"}>>>='0.0 -6285710 -6285710'
  [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = 0
  end_time =0.15
  dt = 0.001
  dtmin = 0.0000001
  timestep_tolerance = 1e-8
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./deformation]
    type = ComputeIsolatorDeformation<<<{"description": "Compute the deformations and rotations in a two-noded isolator element.", "href": "../../source/materials/ComputeIsolatorDeformation.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    sd_ratio<<<{"description": "Shear distance ratio."}>>> = 0.5
    y_orientation<<<{"description": "Orientation of the local Y direction along which, Ky is provided. This should be perpendicular to the axis of the isolator."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    rotations<<<{"description": "The rotation variables appropriate for the simulation geometry and coordinate system."}>>> = 'rot_x rot_y rot_z'
    velocities<<<{"description": "Translational velocity variables."}>>> = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeFPIsolatorElasticity<<<{"description": "Compute the forces and the stiffness matrix for a single concave Friction Pendulum isolator element.", "href": "../../source/materials/ComputeFPIsolatorElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    mu_ref<<<{"description": "Reference co-efficient of friction."}>>> = 0.06
    p_ref<<<{"description": "Reference axial pressure."}>>> = 50e6
    diffusivity<<<{"description": "Thermal diffusivity of steel."}>>> = 4.4e-6
    conductivity<<<{"description": "Thermal conductivity of steel."}>>> = 18
    a<<<{"description": "Rate parameter."}>>> = 100
    r_eff<<<{"description": "Effective radius of curvature of sliding surface."}>>> = 2.2352
    r_contact<<<{"description": "Radius of contact area at sliding surface."}>>> = 0.2
    uy<<<{"description": "Yield displacement of the bearing in shear."}>>> = 0.001
    unit<<<{"description": "Tag for conversion in the pressure factor computation when different unit systems are used. Enter 1 for N m s C;  2 for kN m s C;  3 for N mm s C;  4 for kN mm s C;  5 for lb in s C;  6 for kip in s C;  7 for lb ft s C;  8 for kip ft s C. "}>>> = 1
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
    pressure_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous pressure."}>>> = true
    temperature_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous temperature."}>>> = true
    velocity_dependent<<<{"description": "Switch for modeling friction dependence on the instantaneous sliding velocity."}>>> = true
  [../]
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./disp_x0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = disp_x
  [../]
  [./vel_x0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = vel_x
  [../]
  [./accel_x0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = accel_x
  [../]
  [./disp_x1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_x
  [../]
  [./vel_x1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_x
  [../]
  [./accel_x1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_x
  [../]
  [./reaction_x]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./disp_y0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = disp_y
  [../]
  [./vel_y0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = vel_y
  [../]
  [./accel_y0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = accel_y
  [../]
  [./disp_y1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_y
  [../]
  [./vel_y1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_y
  [../]
  [./accel_y1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_y
  [../]
  [./reaction_y]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_y
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
  [./disp_z0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = disp_z
  [../]
  [./vel_z0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = vel_z
  [../]
  [./accel_z0]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 0
    variable<<<{"description": "The variable to be monitored"}>>> = accel_z
  [../]
  [./disp_z1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_z
  [../]
  [./vel_z1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_z
  [../]
  [./accel_z1]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_z
  [../]
  [./reaction_z]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_z
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
[]

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
  interval=1
[]

(test/tests/materials/fp_isolator/fp_isolator_seismic_PTV.i)

The figures below show the response of the FP bearing to the prescribed seismic loading. The local co-ordinate system for the FP bearing can be identified here.

Figure 10: Response of the FP bearing in the shear (local y) direction to the prescribed seismic loading ().

Figure 11: Response of the FP bearing in the shear (local z) direction to the prescribed seismic loading ().

Nonlinear Fluid Viscous Damper

ComputeFVDamperElasticity material is used to simulate the hysteretic response of a nonlinear fluid viscous damper (FVD) and is used with two-node link type elements in MASTODON. For each subdomain (that may contain multiple link elements), the material properties are defined by creating the material block, ComputeFVDamperElasticity, and the kernel block, StressDivergenceDamper. Sample information is shown in the input file below.

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./elasticity]
    type = ComputeFVDamperElasticity<<<{"description": "Compute the deformations, forces and the stiffness matrix corresponding to a two-node nonlinear fluid viscous damper element.", "href": "../../source/materials/ComputeFVDamperElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    y_orientation<<<{"description": "Orientation of the y direction along with Ky is provided. This should be perpendicular to the axis of the Damper."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation of geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    cd<<<{"description": "Damping co-efficient."}>>> = 2226502
    alpha<<<{"description": "Velocity exponent of the damper."}>>> = 0.3
    k<<<{"description": "Axial stiffness of the damper assembly."}>>> =300000000
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixy0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./disp_x_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    function<<<{"description": "Function describing the displacement."}>>> = displacement
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = accel_x
    velocity<<<{"description": "The velocity variable."}>>> = vel_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./displacement]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = disp_axial.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = -0.02
  end_time = 2
  dt = 0.0025
  dtmin = 0.00001
  timestep_tolerance = 1e-6
[]

A description of each of the input parameters is provided in the syntax description. Additionally, the response of the nonlinear FVD to static and seismic loading is demonstrated in the examples described below. Analysis results are compared with verified and validated numerical models implemented in the open source finite element package, OpenSees (Mazzoni et al. (2009)).

Response to static loading

The input file below performs the analysis of a nonlinear FVD subjected to a cyclic loading in the axial direction. A sinusoidal displacement shown in Figure 12, with increasing amplitude of 12, 24 and 36 mm, at a frequency of 0.5Hz is applied to the top node of the damper in the axial direction, and the bottom node is restrained in all three degrees-of-freedom.

# Test for Damper in Axial (Sinewave loading)

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
  displacements<<<{"description": "The variables corresponding to the x y z displacements of the mesh.  If this is provided then the displacements will be taken into account during the computation. Creation of the displaced mesh can be suppressed even if this is set by setting 'use_displaced_mesh = false'."}>>> = 'disp_x disp_y disp_z'
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./disp_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./lr_disp_x]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '0'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./elasticity]
    type = ComputeFVDamperElasticity<<<{"description": "Compute the deformations, forces and the stiffness matrix corresponding to a two-node nonlinear fluid viscous damper element.", "href": "../../source/materials/ComputeFVDamperElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    y_orientation<<<{"description": "Orientation of the y direction along with Ky is provided. This should be perpendicular to the axis of the Damper."}>>> = '0.0 1.0 0.0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation of geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    cd<<<{"description": "Damping co-efficient."}>>> = 2226502
    alpha<<<{"description": "Velocity exponent of the damper."}>>> = 0.3
    k<<<{"description": "Axial stiffness of the damper assembly."}>>> =300000000
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./fixx0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixy0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fixz0]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./disp_x_1]
    type = PresetDisplacement<<<{"description": "Prescribe the displacement on a given boundary in a given direction.", "href": "../../source/bcs/PresetDisplacement.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    function<<<{"description": "Function describing the displacement."}>>> = displacement
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = accel_x
    velocity<<<{"description": "The velocity variable."}>>> = vel_x
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./displacement]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = disp_axial.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = -0.02
  end_time = 2
  dt = 0.0025
  dtmin = 0.00001
  timestep_tolerance = 1e-6
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./disp_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = disp_x
  [../]
  [./vel_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = vel_x
  [../]
  [./accel_x]
    type = NodalVariableValue<<<{"description": "Outputs values of a nodal variable at a particular location", "href": "../../source/postprocessors/NodalVariableValue.html"}>>>
    nodeid<<<{"description": "The ID of the node where we monitor"}>>> = 1
    variable<<<{"description": "The variable to be monitored"}>>> = accel_x
  [../]
  [./reaction_x]
    type = NodalSum<<<{"description": "Computes the sum of all of the nodal values of the specified variable. Note: This object sets the default \"unique_node_execute\" flag to true to avoid double counting nodes between shared blocks.", "href": "../../source/postprocessors/NodalSum.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = reaction_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = left
  [../]
[]

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  interval = 2
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
[]

(test/tests/materials/fv_damper/fv_damper_axial.i)

Figure 12: Displacement loading history along the axial direction of the damper.

Four test cases are run for varying and , and the axial stiffness () of the damper is held constant.The values presented below are in SI units. The response of the nonlinear FVD element to this prescribed cyclic loading in the axial direction is shown in Figure 13

Figure 13: Axial response of the nonlinear FVD to the prescribed cyclic loading for varying and .

Response to seismic loading

The input file below, demonstrates the seismic response a single bay portal frame installed with a diagonal nonlinear FVD element. The beam-columns are modeled using Euler-Bernoulli beam formulation and are assumed to behave linear elastic. A total mass of 50 tons is lumped at the floor level nodes to simulate the reactive mass. LineElementMaster is used to simplify the input file syntax for creating beam and column elements. The mesh adopted for beam and column elements is identified in Figure 14.

# Test for a protal frame installed with a diagonal Fluid Viscous Damper element
# The mesh for the geometry is imported from exodus file "fv_damper_frame.e"
# Beam-column elements are modeled as Euler-Bernouli beam elements

# Dimesnions
# columns
# E = 20e9, G = 100e9, A = 9e-2, Iy = Iz = 6.75e-4

# Beams
# E = 20e9, G = 100e9, A = 9e-2, Iy = Iz = 6.75e-1 (I_beam = 1000*I_Column to simulate rigid beam)

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = FileMesh
  file = 'fv_damper_frame.e'
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./disp_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./disp_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./rot_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
    block = '1 2'
  [../]
  [./rot_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
    block = '1 2'
  [../]
  [./rot_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
    block = '1 2'
  [../]
[]

[AuxVariables<<<{"href": "../../syntax/AuxVariables/index.html"}>>>]
  [./vel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./vel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_x]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_y]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./accel_z]
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = LAGRANGE
  [../]
  [./reaction_x]
    block = '1 2 3'
  [../]
  [./reaction_y]
    block = '1 2 3'
  [../]
  [./reaction_z]
    block = '1 2 3'
  [../]
  [./reaction_xx]
    block = '1 2 3'
  [../]
  [./reaction_yy]
    block = '1 2 3'
  [../]
  [./reaction_zz]
    block = '1 2 3'
  [../]
[]

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [./accel_x]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_x
    displacement<<<{"description": "displacement variable"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_y
    displacement<<<{"description": "displacement variable"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux<<<{"description": "Computes the current acceleration using the Newmark method.", "href": "../../source/auxkernels/NewmarkAccelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = accel_z
    displacement<<<{"description": "displacement variable"}>>> = disp_z
    velocity<<<{"description": "velocity variable"}>>> = vel_z
    beta<<<{"description": "beta parameter for Newmark method"}>>> = 0.25
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux<<<{"description": "Calculates the current velocity using Newmark method.", "href": "../../source/auxkernels/NewmarkVelAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = vel_z
    acceleration<<<{"description": "acceleration variable"}>>> = accel_z
    gamma<<<{"description": "gamma parameter for Newmark method"}>>> = 0.5
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./damper_disp_x]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 0
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_x
  [../]
  [./damper_disp_y]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 1
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_y
  [../]
  [./damper_disp_z]
    type = StressDivergenceDamper<<<{"description": "Kernel for two-noded nonlinear fluid viscous damper element", "href": "../../source/kernels/StressDivergenceDamper.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
    displacements<<<{"description": "The displacement variables for Damper."}>>> = 'disp_x disp_y disp_z'
    component<<<{"description": "An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)."}>>> = 2
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    save_in<<<{"description": "The name of auxiliary variables to save this Kernel's residual contributions to.  Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)"}>>> = reaction_z
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./x_inertial]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    velocity<<<{"description": "velocity variable"}>>> = vel_x
    acceleration<<<{"description": "acceleration variable"}>>> = accel_x
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = '2 3'
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 25000
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> = 0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> = 0
  [../]
  [./y_inertial]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = '2 3'
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 25000
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> = 0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> = 0
  [../]
  [./z_inertial]
    type = NodalTranslationalInertia<<<{"description": "Computes the inertial forces and mass proportional damping terms corresponding to nodal mass.", "href": "../../source/nodalkernels/NodalTranslationalInertia.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    velocity<<<{"description": "velocity variable"}>>> = vel_y
    acceleration<<<{"description": "acceleration variable"}>>> = accel_y
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = '2 3'
    beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25
    gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5
    mass<<<{"description": "Mass associated with the node"}>>> = 25000
    alpha<<<{"description": "Alpha parameter for mass dependent numerical damping induced by HHT time integration scheme"}>>> = 0
    eta<<<{"description": "Constant real number defining the eta parameter for Rayleigh damping."}>>> = 0
  [../]
[]

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>/SolidMechanics<<<{"href": "../../syntax/Physics/SolidMechanics/index.html"}>>>/LineElement<<<{"href": "../../syntax/Physics/SolidMechanics/LineElement/index.html"}>>>/QuasiStatic<<<{"href": "../../syntax/Physics/SolidMechanics/LineElement/QuasiStatic/index.html"}>>>]
  displacements<<<{"description": "The nonlinear displacement variables for the problem"}>>> = 'disp_x disp_y disp_z'
  rotations<<<{"description": "The rotations appropriate for the simulation geometry and coordinate system"}>>> = 'rot_x rot_y rot_z'
  velocities<<<{"description": "Translational velocity variables"}>>> = 'vel_x vel_y vel_z'
  accelerations<<<{"description": "Translational acceleration variables"}>>> = 'accel_x accel_y accel_z'
  rotational_velocities<<<{"description": "Rotational velocity variables"}>>> = 'rot_vel_x rot_vel_y rot_vel_z'
  rotational_accelerations<<<{"description": "Rotational acceleration variables"}>>> = 'rot_accel_x rot_accel_y rot_accel_z'
  save_in<<<{"description": "The displacement and rotational residuals"}>>> = 'reaction_x reaction_y reaction_z'

  beta<<<{"description": "beta parameter for Newmark Time integration"}>>> = 0.25 # Newmark time integration parameter
  gamma<<<{"description": "gamma parameter for Newmark Time integration"}>>> = 0.5 # Newmark time integration parameter

  # parameters for 5% Rayleigh damping
  zeta<<<{"description": "Name of material property or a constant real number defining the zeta parameter for stiffness proportional Rayleigh damping."}>>> = 0  # stiffness proportional damping
  eta<<<{"description": "Name of material property or a constant real number defining the eta parameter for mass proportional Rayleigh damping."}>>> = 0   # Mass proportional Rayleigh damping

  [./block_1]
    block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence, inertia kernels and materials will be applied to"}>>> = 1
    area<<<{"description": "Cross-section area of the beam. Can be supplied as either a number or a variable name."}>>> = 9e-2
    Iy<<<{"description": "Second moment of area of the beam about y axis. Can be supplied as either a number or a variable name."}>>> = 6.75e-4
    Iz<<<{"description": "Second moment of area of the beam about z axis. Can be supplied as either a number or a variable name."}>>> = 6.75e-4
    y_orientation<<<{"description": "Orientation of the y direction along which Iyy is provided. This should be perpendicular to the axis of the beam."}>>> = '0.0 0.0 1.0'
  [../]
  [./block_2]
    block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence, inertia kernels and materials will be applied to"}>>> = 2
    area<<<{"description": "Cross-section area of the beam. Can be supplied as either a number or a variable name."}>>> = 9e-2
    Iy<<<{"description": "Second moment of area of the beam about y axis. Can be supplied as either a number or a variable name."}>>> = 6.75e-1
    Iz<<<{"description": "Second moment of area of the beam about z axis. Can be supplied as either a number or a variable name."}>>> = 6.75e-1
    y_orientation<<<{"description": "Orientation of the y direction along which Iyy is provided. This should be perpendicular to the axis of the beam."}>>> = '0.0 1.0 0.0'
  [../]
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [./elasticity_beamcolumn]
    type = ComputeElasticityBeam<<<{"description": "Computes the equivalent of the elasticity tensor for the beam element, which are vectors of material translational and flexural stiffness.", "href": "../../source/materials/ComputeElasticityBeam.html"}>>>
    youngs_modulus<<<{"description": "Young's modulus of the material. Can be supplied as either a number or a variable name."}>>> = 20e9
    poissons_ratio<<<{"description": "Poisson's ratio of the material. Can be supplied as either a number or a variable name."}>>> = -0.9
    shear_coefficient<<<{"description": "Scale factor for the shear modulus. Can be supplied as either a number or a variable name."}>>> = 1
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2'
  [../]
  [./stress_beam]
    type = ComputeBeamResultants<<<{"description": "Compute forces and moments using elasticity", "href": "../../source/materials/ComputeBeamResultants.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2'
  [../]
  [./elasticity_damper]
    type = ComputeFVDamperElasticity<<<{"description": "Compute the deformations, forces and the stiffness matrix corresponding to a two-node nonlinear fluid viscous damper element.", "href": "../../source/materials/ComputeFVDamperElasticity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
    y_orientation<<<{"description": "Orientation of the y direction along with Ky is provided. This should be perpendicular to the axis of the Damper."}>>> = '-0.5144 0.85749 0'
    displacements<<<{"description": "The displacement variables appropriate for the simulation of geometry and coordinate system."}>>> = 'disp_x disp_y disp_z'
    cd<<<{"description": "Damping co-efficient."}>>> = 232764
    alpha<<<{"description": "Velocity exponent of the damper."}>>> = 0.35
    k<<<{"description": "Axial stiffness of the damper assembly."}>>> = 25000000
    gamma<<<{"description": "Gamma parameter of Newmark algorithm."}>>> = 0.5
    beta<<<{"description": "Beta parameter of Newmark algorithm."}>>> = 0.25
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./base_accel_x]
    type = PresetAcceleration<<<{"description": "Prescribe acceleration on a given boundary in a given direction", "href": "../../source/bcs/PresetAcceleration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    function<<<{"description": "Function describing the velocity."}>>> = acceleration_x
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_x
    beta<<<{"description": "beta parameter for Newmark time integration."}>>> = 0.25
    acceleration<<<{"description": "The acceleration variable."}>>> = 'accel_x'
    velocity<<<{"description": "The velocity variable."}>>> = 'vel_x'
  [../]
  [./fix_y]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fix_z]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = disp_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fix_rot_x]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fix_rot_y]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
  [./fix_rot_z]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "../../source/bcs/DirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = rot_z
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    value<<<{"description": "Value of the BC"}>>> = 0.0
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./acceleration_x]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../../source/functions/PiecewiseLinear.html"}>>>
    data_file<<<{"description": "File holding CSV data"}>>> = acceleration.csv
    format<<<{"description": "Format of csv data file that is in either in columns or rows"}>>> = columns
  [../]
[]

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [./smp]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  start_time = 0
  end_time = 0.2
  dt = 0.0005
  dtmin = 0.000001
  timestep_tolerance = 1e-6
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  # For basicdisp and basicforce postprocessors, divide the output values
  # by a scale factor equal to 'length of the damper element; (5.83 for this
  # problem). Becasue the object 'ElementIntegralMaterialProperty', calculates
  # the material property value integrating over the element length.
  [./basicdisp]
    type = ElementIntegralMaterialProperty<<<{"description": "Compute the integral of the material property over the domain", "href": "../../source/postprocessors/ElementIntegralMaterialProperty.html"}>>>
    mat_prop<<<{"description": "The name of the material property"}>>> = basic_deformation
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
  [../]
  [./basicforce]
    type = ElementIntegralMaterialProperty<<<{"description": "Compute the integral of the material property over the domain", "href": "../../source/postprocessors/ElementIntegralMaterialProperty.html"}>>>
    mat_prop<<<{"description": "The name of the material property"}>>> = basic_force
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '3'
  [../]
  [./disp_bottom_right]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = disp_x
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '5 0 0'
  [../]
  [./disp_top_right]
    type = PointValue<<<{"description": "Compute the value of a variable at a specified location", "href": "../../source/postprocessors/PointValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on."}>>> = disp_x
    point<<<{"description": "The physical point where the solution will be evaluated."}>>> = '5 3 0'
  [../]
[]

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
  perf_graph<<<{"description": "Enable printing of the performance graph to the screen (Console)"}>>> = true
  interval = 10
[]

(test/tests/materials/fv_damper/fv_damper_seismic_frame.i)

Figure 14: Mesh geometry for the portal frame installed with a diagonal nonlinear FVD element.

The ground acceleration is applied at the bottom nodes of the frame using PresetAcceleration boundary condition. The hysteretic response of the nonlinear FVD to the prescribed seismic loading is shown in Figure 15. The response is benchmarked using the results obtained from OpenSees.

Figure 15: Nonlinear hysteretic response of the nonlinear FVD element to the prescribed seismic loading.