Getting Started

This section provides step-by-step instructions to define the basic components of a numerical model for finite element analysis using the MASTODON framework.

Kernels

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

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

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

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

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