References

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
[]

The response of the LR isolator to cyclic loading in the axial direction is shown in Figure 1.

Figure 1: 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
  [../]
[]

The response of the LR isolator to cyclic loading in the shear direction is shown in Figure 2.

Figure 2: 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'
  [../]
[]

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

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

Figure 4: Response of the LR isolator in the shear (local y) direction to the prescribed seismic loading.

Figure 5: Response of the LR isolator in the shear (local z) direction to the prescribed seismic loading.

Dassault Systòmes. Abaqus - finite element analysis software, v2016. 2018.

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

# 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]
  type = GeneratedMesh
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./vel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[AuxKernels]
  [./accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = disp_z
    velocity = vel_z
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = accel_z
    gamma = 0.5
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./fixx0]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./fixy0]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0.0
  [../]
  [./fixz0]
    type = DirichletBC
    variable = disp_z
    boundary = left
    value = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC
    variable = rot_x
    boundary = left
    value = 0.0
  [../]
  [./fixry0]
    type = DirichletBC
    variable = rot_y
    boundary = left
    value = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC
    variable = rot_z
    boundary = left
    value = 0.0
  [../]
  [./fixrx1]
    type = DirichletBC
    variable = rot_x
    boundary = right
    value = 0.0
  [../]
  [./fixry1]
    type = DirichletBC
    variable = rot_y
    boundary = right
    value = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC
    variable = rot_z
    boundary = right
    value = 0.0
  [../]
  [./disp_x_1]
    type = PresetDisplacement
    boundary = right
    function = history_disp_axial
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
  [./disp_y_1]
    type = PresetDisplacement
    boundary = right
    function = history_disp_shear
    variable = disp_y
    beta = 0.25
    acceleration = accel_y
    velocity = vel_y
  [../]
[]

[Functions]
  [./history_disp_axial]
    type = PiecewiseLinear
    data_file = disp_axial_ct.csv
    format = columns
  [../]
  [./history_disp_shear]
    type = PiecewiseLinear
    x = '0.0 10.0'
    y = '0.0 0.3048'
    [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  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]
  [./lr_disp_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 0
    variable = disp_x
    save_in = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 1
    variable = disp_y
    save_in = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 2
    variable = disp_z
    save_in = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 3
    variable = rot_x
    save_in = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 4
    variable = rot_y
    save_in = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 5
    variable = rot_z
    save_in = reaction_zz
  [../]
[]

[Materials]
  [./deformation]
    type = ComputeIsolatorDeformation
    block = 0
    sd_ratio = 0.5
    y_orientation = '0.0 1.0 0.0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    velocities = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeLRIsolatorElasticity
    block = 0
    fy = 207160
    alpha = 0.03812
    G_rubber = 0.87e6
    K_rubber = 2e9
    D1 = 0.1397
    D2 = 0.508
    ts = 0.00476
    tr = 0.009525
    n = 16
    tc = 0.0127
    kc = 20
    phi_m = 0.75
    ac = 1
    cd = 0
    gamma = 0.5
    beta = 0.25
    k_steel = 50
    a_steel = 1.41e-5
    rho_lead = 11200
    c_lead = 130
    cavitation = true
    horizontal_stiffness_variation = true
    vertical_stiffness_variation = true
    strength_degradation = true
    buckling_load_variation = true
  [../]
[]

[Postprocessors]
  [./disp_x]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_x
  [../]
  [./vel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_x
  [../]
  [./accel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_x
  [../]
  [./reaction_x]
    type = NodalSum
    variable = reaction_x
    boundary = left
  [../]
  [./disp_y]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_y
  [../]
  [./vel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_y
  [../]
  [./accel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_y
  [../]
  [./reaction_y]
    type = NodalSum
    variable = reaction_y
    boundary = left
  [../]
  [./disp_z]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_z
  [../]
  [./vel_z]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_z
  [../]
  [./accel_z]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_z
  [../]
  [./reaction_z]
    type = NodalSum
    variable = reaction_z
    boundary = left
  [../]
  [./reaction_xx]
    type = NodalSum
    variable = reaction_xx
    boundary = left
  [../]
  [./reaction_yy]
    type = NodalSum
    variable = reaction_yy
    boundary = left
  [../]
  [./reaction_zz]
    type = NodalSum
    variable = reaction_zz
    boundary = left
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

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

# 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]
  type = GeneratedMesh
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./vel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[AuxKernels]
  [./accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = disp_z
    velocity = vel_z
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = accel_z
    gamma = 0.5
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./fixx0]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./fixy0]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0.0
  [../]
  [./fixz0]
    type = DirichletBC
    variable = disp_z
    boundary = left
    value = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC
    variable = rot_x
    boundary = left
    value = 0.0
  [../]
  [./fixry0]
    type = DirichletBC
    variable = rot_y
    boundary = left
    value = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC
    variable = rot_z
    boundary = left
    value = 0.0
  [../]
  [./fixrx1]
    type = DirichletBC
    variable = rot_x
    boundary = right
    value = 0.0
  [../]
  [./fixry1]
    type = DirichletBC
    variable = rot_y
    boundary = right
    value = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC
    variable = rot_z
    boundary = right
    value = 0.0
  [../]
  [./disp_x_1]
    type = PresetDisplacement
    boundary = right
    function = history_disp_axial
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
  [./disp_y_1]
    type = PresetDisplacement
    boundary = right
    function = history_disp_shear
    variable = disp_y
    beta = 0.25
    acceleration = accel_y
    velocity = vel_y
  [../]
[]

[Functions]
  [./history_disp_axial]
    type = PiecewiseLinear
    data_file = disp_axial_ct.csv
    format = columns
  [../]
  [./history_disp_shear]
    type = PiecewiseLinear
    x = '0.0 10.0'
    y = '0.0 0.3048'
    [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  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]
  [./lr_disp_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 0
    variable = disp_x
    save_in = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 1
    variable = disp_y
    save_in = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 2
    variable = disp_z
    save_in = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 3
    variable = rot_x
    save_in = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 4
    variable = rot_y
    save_in = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 5
    variable = rot_z
    save_in = reaction_zz
  [../]
[]

[Materials]
  [./deformation]
    type = ComputeIsolatorDeformation
    block = 0
    sd_ratio = 0.5
    y_orientation = '0.0 1.0 0.0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    velocities = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeLRIsolatorElasticity
    block = 0
    fy = 207160
    alpha = 0.03812
    G_rubber = 0.87e6
    K_rubber = 2e9
    D1 = 0.1397
    D2 = 0.508
    ts = 0.00476
    tr = 0.009525
    n = 16
    tc = 0.0127
    kc = 20
    phi_m = 0.75
    ac = 1
    cd = 0
    gamma = 0.5
    beta = 0.25
    k_steel = 50
    a_steel = 1.41e-5
    rho_lead = 11200
    c_lead = 130
    cavitation = true
    horizontal_stiffness_variation = true
    vertical_stiffness_variation = true
    strength_degradation = true
    buckling_load_variation = true
  [../]
[]

[Postprocessors]
  [./disp_x]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_x
  [../]
  [./vel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_x
  [../]
  [./accel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_x
  [../]
  [./reaction_x]
    type = NodalSum
    variable = reaction_x
    boundary = left
  [../]
  [./disp_y]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_y
  [../]
  [./vel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_y
  [../]
  [./accel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_y
  [../]
  [./reaction_y]
    type = NodalSum
    variable = reaction_y
    boundary = left
  [../]
  [./disp_z]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_z
  [../]
  [./vel_z]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_z
  [../]
  [./accel_z]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_z
  [../]
  [./reaction_z]
    type = NodalSum
    variable = reaction_z
    boundary = left
  [../]
  [./reaction_xx]
    type = NodalSum
    variable = reaction_xx
    boundary = left
  [../]
  [./reaction_yy]
    type = NodalSum
    variable = reaction_yy
    boundary = left
  [../]
  [./reaction_zz]
    type = NodalSum
    variable = reaction_zz
    boundary = left
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

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

# Test for lead rubber isolator in shear

#Loading conditions

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

[Mesh]
  type = GeneratedMesh
  displacements = 'disp_x disp_y disp_z'
  xmin = 0
  xmax = 1
  nx = 1
  dim = 1
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./vel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]

[AuxKernels]
  [./accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = 'disp_x'
    velocity = 'vel_x'
    beta = 0.25
    execute_on = 'timestep_end'
  [../]
  [./vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = 'accel_x'
    gamma = 0.5
    execute_on = 'timestep_end'
  [../]
  [./accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = 'disp_y'
    velocity = 'vel_y'
    beta = 0.25
    execute_on = 'timestep_end'
  [../]
  [./vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = 'accel_y'
    gamma = 0.5
    execute_on = 'timestep_end'
  [../]
  [./accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = 'disp_z'
    velocity = 'vel_z'
    beta = 0.25
    execute_on = 'timestep_end'
  [../]
  [./vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = 'accel_z'
    gamma = 0.5
    execute_on = 'timestep_end'
  [../]
[]

[BCs]
  [./fixx0]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  [../]
  [./fixy0]
    type = DirichletBC
    variable = disp_y
    boundary = 'left'
    value = 0.0
  [../]
  [fixz0]
    type = DirichletBC
    variable = disp_z
    boundary = 'left'
    value = 0.0
  [../]
  [./fixrx0]
    type = DirichletBC
    variable = rot_x
    boundary = 'left'
    value = 0.0
  [../]
  [./fixry0]
    type = DirichletBC
    variable = rot_y
    boundary = 'left'
    value = 0.0
  [../]
  [./fixrz0]
    type = DirichletBC
    variable = rot_z
    boundary = 'left'
    value = 0.0
  [../]
  [fixrx1]
    type = DirichletBC
    variable = rot_x
    boundary = 'right'
    value = 0.0
  [../]
  [./fixry1]
    type = DirichletBC
    variable = rot_y
    boundary = 'right'
    value = 0.0
  [../]
  [./fixrz1]
    type = DirichletBC
    variable = rot_z
    boundary = 'right'
    value = 0.0
  [../]
  [./disp_y_1]
    type = PresetDisplacement
    boundary = 'right'
    variable = disp_y
    function = history_shear_dispy
    beta = 0.25
    acceleration = 'accel_y'
    velocity = 'vel_y'
  [../]
[]

[NodalKernels]
  [./force_x]
    type = UserForcingFunctionNodalKernel
    variable = disp_x
    boundary = 'right'
    function = force_x
  [../]
[]

[Functions]
  [./force_x]
    type = PiecewiseLinear
    x = '0.0 1.0  11.0'
    y = '0.0 -1439520 -1439520'
  [../]
  [./history_shear_dispy]
    type = PiecewiseLinear
    data_file = disp_shear.csv
    format = columns
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  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 = 0.0001
  timestep_tolerance = 1e-6
[]

[Kernels]
  [./lr_disp_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 0
    variable = disp_x
    save_in = 'reaction_x'
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 1
    variable = disp_y
    save_in = 'reaction_y'
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 2
    variable = disp_z
    save_in = 'reaction_z'
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 3
    variable = rot_x
    save_in = 'reaction_xx'
  [../]
  [lr_rot_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 4
    variable = rot_y
    save_in = 'reaction_yy'
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 5
    variable = rot_z
    save_in = 'reaction_zz'
  [../]
[]

[Materials]
  [./deformation]
    type = ComputeIsolatorDeformation
    block = '0'
    sd_ratio = 0.5
    y_orientation = '0.0 1.0 0.0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    velocities = 'vel_x vel_y vel_z'
  [../]
  [./elasticity]
    type = ComputeLRIsolatorElasticity
    block = '0'
    fy = 207155
    alpha = 0.0381
    G_rubber = 0.87e6
    K_rubber = 2e9
    D1 = 0.1397
    D2 = 0.508
    ts = 0.00476
    tr = 0.009525
    n = 16
    tc = 0.0127
    kc = 15
    phi_m = 0.75
    ac = 1
    cd = 128000
    gamma = 0.5
    beta = 0.25
    k_steel = 50
    a_steel = 1.41e-5
    rho_lead = 11200
    c_lead = 130
    cavitation = true
    horizontal_stiffness_variation = true
    vertical_stiffness_variation = true
    strength_degradation = true
    buckling_load_variation = true
  [../]
[]

[Postprocessors]
  [./disp_x]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_x
  [../]
  [./vel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_x
  [../]
  [./accel_x]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_x
  [../]
  [./reaction_x]
    type = NodalSum
    variable = 'reaction_x'
    boundary = 'left'
  [../]
  [./disp_y]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_y
  [../]
  [./vel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = vel_y
  [../]
  [accel_y]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_y
  [../]
  [./reaction_y]
    type = NodalSum
    variable = 'reaction_y'
    boundary = 'left'
  [../]
  [./disp_z]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_z
  [../]
  [./accel_z]
    type = NodalVariableValue
    nodeid = 1
    variable = accel_z
  [../]
  [./reaction_z]
    type = NodalSum
    variable = 'reaction_z'
    boundary = 'left'
  [../]
  [./reaction_xx]
    type = NodalSum
    variable = 'reaction_xx'
    boundary = 'left'
  [../]
  [./reaction_yy]
    type = NodalSum
    variable = 'reaction_yy'
    boundary = 'left'
  [../]
  [./reaction_zz]
    type = NodalSum
    variable = 'reaction_zz'
    boundary = 'left'
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

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

# Test for lead rubber isolator under seismic loading

#Loading conditions

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

[Mesh]
  type = GeneratedMesh
  xmin = 0
  xmax = 0.224
  nx =  1
  dim = 1
  displacements = 'disp_x disp_y disp_z'
[]

[Controls]
  [./C1]
    type = TimePeriod
    disable_objects = '*::x_inertial1 *::y_inertial1 *::z_inertial1 *::vel_x *::vel_y *::vel_z *::accel_x *::accel_y *::accel_z'
    start_time = '0'
    end_time = '0.10'
  [../]
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./vel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./vel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./accel_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./reaction_x]
  [../]
  [./reaction_y]
  [../]
  [./reaction_z]
  [../]
  [./reaction_xx]
  [../]
  [./reaction_yy]
  [../]
  [./reaction_zz]
  [../]
[]


[Kernels]
  [./lr_disp_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 0
    variable = disp_x
    save_in = reaction_x
  [../]
  [./lr_disp_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 1
    variable = disp_y
    save_in = reaction_y
  [../]
  [./lr_disp_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 2
    variable = disp_z
    save_in = reaction_z
  [../]
  [./lr_rot_x]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 3
    variable = rot_x
    save_in = reaction_xx
  [../]
  [./lr_rot_y]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 4
    variable = rot_y
    save_in = reaction_yy
  [../]
  [./lr_rot_z]
    type = StressDivergenceIsolator
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    component = 5
    variable = rot_z
    save_in = reaction_zz
  [../]
[]

[AuxKernels]
  [./accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = timestep_end
  [../]
  [./accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = disp_z
    velocity = vel_z
    beta = 0.25
    execute_on = timestep_end
  [../]
  [./vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = accel_z
    gamma = 0.5
    execute_on = timestep_end
  [../]
[]

[BCs]
[./fixx0]
  type = DirichletBC
  variable = disp_x
  boundary = left
  value = 0.0
[../]
[./fixy0]
  type = DirichletBC
  variable = disp_y
  boundary = left
  value = 0.0
[../]
[./fixz0]
  type = DirichletBC
  variable = disp_z
  boundary = left
  value = 0.0
[../]
[./fixrx0]
  type = DirichletBC
  variable = rot_x
  boundary = left
  value = 0.0
[../]
[./fixry0]
  type = DirichletBC
  variable = rot_y
  boundary = left
  value = 0.0
[../]
[./fixrz0]
  type = DirichletBC
  variable = rot_z
  boundary = left
  value = 0.0
[../]
[./fixrx1]
  type = DirichletBC
  variable = rot_x
  boundary = right
  value = 0.0
[../]
[./fixry1]
  type = DirichletBC
  variable = rot_y
  boundary = right
  value = 0.0
[../]
[./fixrz1]
  type = DirichletBC
  variable = rot_z
  boundary = right
  value = 0.0
[../]
[./accel_x0]
    type = PresetAcceleration
    boundary = 'left'
    function = acceleration_x
    variable = disp_x
    beta = 0.25
    acceleration = 'accel_x'
    velocity = 'vel_x'
[../]
[./accel_y0]
    type = PresetAcceleration
    boundary = 'left'
    function = acceleration_y
    variable = disp_y
    beta = 0.25
    acceleration = 'accel_y'
    velocity = 'vel_y'
[../]
[./accel_z0]
    type = PresetAcceleration
    boundary = 'left'
    function = acceleration_z
    variable = disp_z
    beta = 0.25
    acceleration = 'accel_z'
    velocity = 'vel_z'
[../]
[]

[NodalKernels]
[./x_inertial1]
  type = NodalTranslationalInertia
  variable = disp_x
  velocity = vel_x
  acceleration = accel_x
  boundary = right
  beta = 0.25
  gamma = 0.5
  mass = 146890
  alpha =0
  eta =0
[../]
[./y_inertial1]
  type = NodalTranslationalInertia
  variable = disp_y
  velocity = vel_y
  acceleration = accel_y
  boundary = right
  beta = 0.25
  gamma = 0.5
  mass = 146890
  alpha =0
  eta =0
[../]
[./z_inertial1]
  type = NodalTranslationalInertia
  variable = disp_z
  velocity = vel_z
  acceleration = accel_z
  boundary = right
  beta = 0.25
  gamma = 0.5
  mass = 146890
  alpha =0
  eta =0
[../]

[./force_x]
  type = UserForcingFunctionNodalKernel
  variable = disp_x
  boundary = 'right'
  function = force_x
  [../]
[]

[Functions]
[./acceleration_x]
  type = PiecewiseLinear
  data_file = accel_x.csv
  format=columns
[../]
[./acceleration_y]
  type = PiecewiseLinear
  data_file = accel_y.csv
  format=columns
[../]
[./acceleration_z]
  type = PiecewiseLinear
  data_file = accel_z.csv
  format=columns
[../]
[./force_x]
  type = PiecewiseLinear
  x='0.0 0.05 50'
  y='0.0 -1468900 -1468900'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  line_search = none
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-4
  start_time = 0
  end_time = 0.125
  dt = 1e-4
  dtmin = 1e-7
  timestep_tolerance = 1e-8
[]

[Materials]
[./deformation]
  type = ComputeIsolatorDeformation
  block = '0'
  sd_ratio = 0.5
  y_orientation = '0.0 1.0 0.0'
  displacements = 'disp_x disp_y disp_z'
  rotations = 'rot_x rot_y rot_z'
  velocities = 'vel_x vel_y vel_z'
[../]
[./elasticity]
  type = ComputeLRIsolatorElasticity
  block = '0'
  fy = 207155
  alpha = 0.0381
  G_rubber = 0.87e6
  K_rubber = 2e9
  D1 = 0.1397
  D2 = 0.508
  ts = 0.00476
  tr = 0.009525
  n = 16
  tc = 0.0127
  kc = 20
  phi_m = 0.75
  ac = 1
  cd = 128000
  gamma = 0.5
  beta = 0.25
  k_steel = 50
  a_steel = 1.41e-5
  rho_lead = 11200
  c_lead = 130
  cavitation = true
  horizontal_stiffness_variation = true
  vertical_stiffness_variation = true
  strength_degradation = true
  buckling_load_variation = true
  [../]
[]

[Postprocessors]
[./disp_x0]
  type = NodalVariableValue
  nodeid = 0
  variable = disp_x
[../]
[./vel_x0]
  type = NodalVariableValue
  nodeid = 0
  variable = vel_x
[../]
[./accel_x0]
  type = NodalVariableValue
  nodeid = 0
  variable = accel_x
[../]
[./disp_x1]
  type = NodalVariableValue
  nodeid = 1
  variable = disp_x
[../]
[./vel_x1]
  type = NodalVariableValue
  nodeid = 1
  variable = vel_x
[../]
[./accel_x1]
  type = NodalVariableValue
  nodeid = 1
  variable = accel_x
[../]
[./reaction_x]
  type = NodalSum
  variable = reaction_x
  boundary = left
[../]
[./disp_y0]
  type = NodalVariableValue
  nodeid = 0
  variable = disp_y
[../]
[./vel_y0]
  type = NodalVariableValue
  nodeid = 0
  variable = vel_y
[../]
[./accel_y0]
  type = NodalVariableValue
  nodeid = 0
  variable = accel_y
[../]
[./disp_y1]
  type = NodalVariableValue
  nodeid = 1
  variable = disp_y
[../]
[./vel_y1]
  type = NodalVariableValue
  nodeid = 1
  variable = vel_y
[../]
[./accel_y1]
  type = NodalVariableValue
  nodeid = 1
  variable = accel_y
[../]
[./reaction_y]
  type = NodalSum
  variable = reaction_y
  boundary = left
[../]
[./disp_z0]
  type = NodalVariableValue
  nodeid = 0
  variable = disp_z
[../]
[./vel_z0]
  type = NodalVariableValue
  nodeid = 0
  variable = vel_z
[../]
[./accel_z0]
  type = NodalVariableValue
  nodeid = 0
  variable = accel_z
[../]
[./disp_z1]
  type = NodalVariableValue
  nodeid = 1
  variable = disp_z
[../]
[./vel_z1]
  type = NodalVariableValue
  nodeid = 1
  variable = vel_z
[../]
[./accel_z1]
  type = NodalVariableValue
  nodeid = 1
  variable = accel_z
[../]
[./reaction_z]
  type = NodalSum
  variable = reaction_z
  boundary = left
[../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
  # interval = 10
[]

References

Usage

Development

Demonstration

Lead-Rubber Isolator

Example 1: Response to axial loading

Example 2: Response to shear loading

Example 3: Response to seismic loading

References