ComputeLRIsolatorElasticity

Compute the forces and the stiffness matrix for an LR isolator element.

Description

This material object calculates the force vector and the stiffness matrix of a lead-rubber isolator, when modeled using a two-noded link element. This material uses the formulation developed by Kumar et al. (2015). Further information regarding this formulation and its implementation in MASTODON is presented in the theory and user manuals.

Input Parameters

D1Diameter of lead core.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Diameter of lead core.
D2Outer diameter of the bearing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Outer diameter of the bearing.
G_rubberShear modulus of rubber.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Shear modulus of rubber.
K_rubberBulk modulus of rubber.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Bulk modulus of rubber.
alphaRatio of post-yield shear stiffness to the initial elastic shear stiffness of the bearing. This is dimensionless
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Ratio of post-yield shear stiffness to the initial elastic shear stiffness of the bearing. This is dimensionless
betaBeta parameter of Newmark algorithm.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Beta parameter of Newmark algorithm.
fyYield strength of the bearing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Yield strength of the bearing.
gammaGamma parameter of Newmark algorithm.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Gamma parameter of Newmark algorithm.
nNumber of rubber layers.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Number of rubber layers.
tcThickness of the rubber cover of the bearing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thickness of the rubber cover of the bearing.
trThickness of a single rubber layer.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thickness of a single rubber layer.
tsThickness of a single steel shim.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thickness of a single steel shim.

Required Parameters

a_steel1.41e-05Thermal diffusivity of steel. Defaults to 1.41e-05 m2/s.
Default:1.41e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermal diffusivity of steel. Defaults to 1.41e-05 m2/s.
ac1Strength degradation parameter.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Strength degradation parameter.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
buckling_load_variationFalseSwitch for modeling buckling load variation during the analysis.
Default:False
C++ Type:bool
Controllable:No
Description:Switch for modeling buckling load variation during the analysis.
c_lead130Specific heat capacity of lead. Defaults to 130.0 N-m/kg oC.
Default:130
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Specific heat capacity of lead. Defaults to 130.0 N-m/kg oC.
cavitationFalseSwitch for modeling cavitation and post-cavitation.
Default:False
C++ Type:bool
Controllable:No
Description:Switch for modeling cavitation and post-cavitation.
cd0Viscous damping parameter.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Viscous damping parameter.
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onELEMENTWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:ELEMENT
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
horizontal_stiffness_variationFalseSwitch for modeling variation of horizontal stiffness during the analysis.
Default:False
C++ Type:bool
Controllable:No
Description:Switch for modeling variation of horizontal stiffness during the analysis.
k_steel50Thermal conductivity of steel. Defaults to 50.0 W/(m-oC).
Default:50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity of steel. Defaults to 50.0 W/(m-oC).
kc20Cavitation parameter.
Default:20
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Cavitation parameter.
phi_m0.75Damage index.
Default:0.75
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Damage index.
rho_lead11200Density of lead. Defaults to 11200 kg/m3.
Default:11200
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Density of lead. Defaults to 11200 kg/m3.
strength_degradationFalseSwitch for modeling strength degradation due to lead core heating.
Default:False
C++ Type:bool
Controllable:No
Description:Switch for modeling strength degradation due to lead core heating.
vertical_stiffness_variationFalseSwitch for modeling variation of vertical stiffness during the analysis.
Default:False
C++ Type:bool
Controllable:No
Description:Switch for modeling variation of vertical stiffness during the analysis.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/materials/lr_isolator/lr_isolator_tension.i)
(test/tests/materials/lr_isolator/lr_isolator_axial_ct.i)
(test/tests/materials/lr_isolator/lr_isolator_seismic.i)
(test/tests/materials/lr_isolator/lr_isolator_shear.i)
(test/tests/materials/lr_isolator/lr_isolator_PDelta.i)

References

M. Kumar, A. S. Whittaker, and M. C. Constantinou. Seismic isolation of nuclear power plants using elastomeric bearings. Technical Report MCEER-15-0008, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York, 2015.

@article{manishkumarmceer2015a,
    author = "Kumar, M. and Whittaker, A. S. and Constantinou, M. C.",
    title = "Seismic isolation of nuclear power plants using elastomeric bearings",
    journal = "Technical Report MCEER-15-0008, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York",
    year = "2015"
}

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

# Test for lead rubber isolator in Axial (only tension)

#Loading conditions

# i) A cyclic displacement loading in axial tension (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_tension
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
[]

[Functions]
  [./history_disp_tension]
    type = PiecewiseLinear
    data_file = disp_tension.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 = 0.01
  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 = 207155
    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_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
[]

(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_PDelta.i)

# Test for lead rubber isolator
# Axial 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
  [../]
[]

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

[Functions]
  [./force_x]
    type = PiecewiseLinear
    x = '0.0 1.0 5.0'              # time
    y = '0.0 -590156.0 -590156.0'  # force
  [../]
  [./force_y]
    type = PiecewiseLinear
    x = '0.0 1.0 5.0'              # time
    y = '0.0 371188.0 371188.0'    # force
  [../]
[]

[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 = 1.5
  dt = 0.001
  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 = 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 = 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
  [../]
  [./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
  [../]
  [./reaction_y]
    type = NodalSum
    variable = reaction_y
    boundary = left
  [../]
  [./disp_z]
    type = NodalVariableValue
    nodeid = 1
    variable = disp_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
[]

Description
Input Parameters
Input Files
References

Usage

Development

Demonstration