Rank Two Aux

Access a component of a RankTwoTensor

Description

The AuxKernel RankTwoAux is used to save single components of Rank-2 tensors into an AuxVariable for visualization and/or post-processing purposes. An antisymmetric Rank-2 tensor would require nine separate RankTwoAux AuxKernel-AuxVariable pairs to store all of the components of the antisymmetric Rank-2 tensor; six separate AuxKernel-AuxVariable pairs are required to print out all the unique components of a symmetric Rank-2 tensor. Quantities commonly examined with RankTwoAux are stress ( $var element = document.getElementById("moose-equation-f1ab6703-d631-4d8e-b68c-2142f70d9915");katex.render("\\boldsymbol{\\sigma}", element, {displayMode:false,throwOnError:false});$ ) and strain ( $var element = document.getElementById("moose-equation-3c2ffcd4-6891-4557-8f97-a92381875b5b");katex.render("\\boldsymbol{\\epsilon}", element, {displayMode:false,throwOnError:false});$ ).

The RankTwoAux takes as arguments the values of the index_i and the index_j for the single tensor component to save into an AuxVariable. Eq. (1) shows the index values for each Rank-2 tensor component. $(1)var element = document.getElementById("moose-equation-9f30762b-0735-44c8-a1b6-92c6c00036eb");katex.render(" \\sigma_{ij} \\implies \\begin{bmatrix} \\sigma_{00} & \\sigma_{01} & \\sigma_{02} \\\\ \\sigma_{10} & \\sigma_{11} & \\sigma_{12} \\\\ \\sigma_{20} & \\sigma_{21} & \\sigma_{22} \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

If desired, RankTwoAux can be restricted to save data from a Rank-2 tensor at a single specified quadrature point per element. This option is generally used for debugging purposes.

AuxVariable Order

note:Elemental vs Nodal Visualization of Quadrature Field Values

Results will have different quality based on the AuxVariable:

Elemental Constant Monomial Using an AuxVariable with family = MONOMIAL and order = CONSTANT will give a constant value of the AuxVariable for the entire element, which is computed by taking a volume-weighted average of the integration point quantities. This is the default option using TensorMechanics Action and requires the least computational cost.
Elemental Higher-order Monomial Using an AuxVariable with family = MONOMIAL and order = FIRST or higher will result in fields that vary linearly (or with higher order) within each element. Because the Exodus mesh format does not support higher-order elemental variables, these AuxVariables are output by libMesh as nodal variables for visualization purposes. Using higher order monomial variables in this way can produce smoother visualizations of results for a properly converged simulation.
Nodal Lagrange Using an AuxVariable with family = LAGRANGE will result in a smooth nodal field of the material property, constructed using nodal patch recovery. patch_polynomial_order is set to equal the order of the AuxVariable by default. Use this option for the best (smoothest, most accurate) results, but there is some additional computational cost. Furthermore, this method is suitable only for serial simulations at present.

Example Input File Syntax

[./stress_xy]
  type = RankTwoAux
  rank_two_tensor = stress
  variable = stress_xy
  index_i = 0
  index_j = 1
[../]

An AuxVariable is required to store the RankTwoAux AuxKernel information. Note that the name of the AuxVariable is used as the argument for the variable input parameter in the RankTwoAux block.

[./stress_xy]
  order = CONSTANT
  family = MONOMIAL
[../]

Input Parameters

index_iThe index i of ij for the tensor to output (0, 1, 2)
C++ Type:unsigned int
Controllable:No
Description:The index i of ij for the tensor to output (0, 1, 2)
index_jThe index j of ij for the tensor to output (0, 1, 2)
C++ Type:unsigned int
Controllable:No
Description:The index j of ij for the tensor to output (0, 1, 2)
rank_two_tensorThe rank two material tensor name
C++ Type:MaterialPropertyName
Controllable:No
Description:The rank two material tensor name
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

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
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
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
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.

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.
patch_polynomial_orderPolynomial order used in least squares fitting of material property over the local patch of elements connected to a given node
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH
Controllable:No
Description:Polynomial order used in least squares fitting of material property over the local patch of elements connected to a given node
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
selected_qpEvaluate the tensor at this specific quadpoint
C++ Type:unsigned int
Controllable:No
Description:Evaluate the tensor at this specific quadpoint
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

(moose/modules/tensor_mechanics/test/tests/elastic_patch/elastic_patch.i)

# Patch Test

# This test is designed to compute constant xx, yy, zz, xy, yz, and zx
#  stress on a set of irregular hexes.  The mesh is composed of one
#  block with seven elements.  The elements form a unit cube with one
#  internal element.  There is a nodeset for each exterior node.

# The cube is displaced by 1e-6 units in x, 2e-6 in y, and 3e-6 in z.
#  The faces are sheared as well (1e-6, 2e-6, and 3e-6 for xy, yz, and
#  zx).  This gives a uniform strain/stress state for all six unique
#  tensor components.

# With Young's modulus at 1e6 and Poisson's ratio at 0, the shear
#  modulus is 5e5 (G=E/2/(1+nu)).  Therefore,
#
#  stress xx = 1e6 * 1e-6 = 1
#  stress yy = 1e6 * 2e-6 = 2
#  stress zz = 1e6 * 3e-6 = 3
#  stress xy = 2 * 5e5 * 1e-6 / 2 = 0.5
#             (2 * G   * gamma_xy / 2 = 2 * G * epsilon_xy)
#  stress yz = 2 * 5e5 * 2e-6 / 2 = 1
#  stress zx = 2 * 5e5 * 3e-6 / 2 = 1.5

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  block = '1 2 3 4 5 6 7'
[]

[Mesh]#Comment
  file = elastic_patch.e
[] # Mesh

[Functions]
  [./rampConstant1]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 1e-6
  [../]
  [./rampConstant2]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 2e-6
  [../]
  [./rampConstant3]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 3e-6
  [../]
  [./rampConstant4]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 4e-6
  [../]
  [./rampConstant6]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 6e-6
  [../]
[] # Functions

[Variables]

  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]

[] # Variables

[AuxVariables]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./hydrostatic]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./firstinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./secondinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./thirdinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./maxprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./midprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./minprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./direction]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./max_shear]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sint]
    order = CONSTANT
    family = MONOMIAL
  [../]

[] # AuxVariables

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
  [../]
[]

[AuxKernels]

  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./elastic_energy]
    type = ElasticEnergyAux
    variable = elastic_energy
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = vonmisesStress
  [../]
  [./hydrostatic]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hydrostatic
    scalar_type = hydrostatic
  [../]
  [./fi]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = firstinv
    scalar_type = firstinvariant
  [../]
  [./si]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = secondinv
    scalar_type = secondinvariant
  [../]
  [./ti]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = thirdinv
    scalar_type = thirdinvariant
  [../]
  [./maxprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = maxprincipal
    scalar_type = MaxPRiNCIpAl
  [../]
  [./midprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = midprincipal
    scalar_type = MidPRiNCIpAl
  [../]
  [./minprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = minprincipal
    scalar_type = MiNPRiNCIpAl
  [../]
  [./direction]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = direction
    scalar_type = direction
    direction = '1 1 1'
  [../]
  [./max_shear]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = max_shear
    scalar_type = MaxShear
  [../]
  [./sint]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = sint
    scalar_type = StressIntensity
  [../]


[] # AuxKernels

[BCs]

  [./node1_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./node1_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1
    function = rampConstant2
  [../]
  [./node1_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 1
    function = rampConstant3
  [../]

  [./node2_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 2
    function = rampConstant1
  [../]
  [./node2_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 2
    function = rampConstant2
  [../]
  [./node2_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 2
    function = rampConstant6
  [../]

  [./node3_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 3
    function = rampConstant1
  [../]
  [./node3_y]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]
  [./node3_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 3
    function = rampConstant3
  [../]

  [./node4_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]
  [./node4_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  [../]
  [./node4_z]
    type = DirichletBC
    variable = disp_z
    boundary = 4
    value = 0.0
  [../]

  [./node5_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 5
    function = rampConstant1
  [../]
  [./node5_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = rampConstant4
  [../]
  [./node5_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 5
    function = rampConstant3
  [../]

  [./node6_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 6
    function = rampConstant2
  [../]
  [./node6_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 6
    function = rampConstant4
  [../]
  [./node6_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 6
    function = rampConstant6
  [../]

  [./node7_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 7
    function = rampConstant3
  [../]

  [./node8_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 8
    function = rampConstant1
  [../]
  [./node8_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 8
    function = rampConstant2
  [../]
  [./node8_z]
    type = DirichletBC
    variable = disp_z
    boundary = 8
    value = 0.0
  [../]


[] # BCs

[Materials]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.0
  [../]

  [./strain]
    type = ComputeFiniteStrain
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

[] # Materials

[Executioner]

  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-10

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 2
  end_time = 2.0
[] # Executioner

[Outputs]
  exodus = true
[] # Outputs

(moose/modules/tensor_mechanics/test/tests/elastic_patch/elastic_patch.i)

# Patch Test

# This test is designed to compute constant xx, yy, zz, xy, yz, and zx
#  stress on a set of irregular hexes.  The mesh is composed of one
#  block with seven elements.  The elements form a unit cube with one
#  internal element.  There is a nodeset for each exterior node.

# The cube is displaced by 1e-6 units in x, 2e-6 in y, and 3e-6 in z.
#  The faces are sheared as well (1e-6, 2e-6, and 3e-6 for xy, yz, and
#  zx).  This gives a uniform strain/stress state for all six unique
#  tensor components.

# With Young's modulus at 1e6 and Poisson's ratio at 0, the shear
#  modulus is 5e5 (G=E/2/(1+nu)).  Therefore,
#
#  stress xx = 1e6 * 1e-6 = 1
#  stress yy = 1e6 * 2e-6 = 2
#  stress zz = 1e6 * 3e-6 = 3
#  stress xy = 2 * 5e5 * 1e-6 / 2 = 0.5
#             (2 * G   * gamma_xy / 2 = 2 * G * epsilon_xy)
#  stress yz = 2 * 5e5 * 2e-6 / 2 = 1
#  stress zx = 2 * 5e5 * 3e-6 / 2 = 1.5

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  block = '1 2 3 4 5 6 7'
[]

[Mesh]#Comment
  file = elastic_patch.e
[] # Mesh

[Functions]
  [./rampConstant1]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 1e-6
  [../]
  [./rampConstant2]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 2e-6
  [../]
  [./rampConstant3]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 3e-6
  [../]
  [./rampConstant4]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 4e-6
  [../]
  [./rampConstant6]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 6e-6
  [../]
[] # Functions

[Variables]

  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]

[] # Variables

[AuxVariables]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./hydrostatic]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./firstinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./secondinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./thirdinv]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./maxprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./midprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./minprincipal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./direction]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./max_shear]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sint]
    order = CONSTANT
    family = MONOMIAL
  [../]

[] # AuxVariables

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
  [../]
[]

[AuxKernels]

  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./elastic_energy]
    type = ElasticEnergyAux
    variable = elastic_energy
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = vonmisesStress
  [../]
  [./hydrostatic]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hydrostatic
    scalar_type = hydrostatic
  [../]
  [./fi]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = firstinv
    scalar_type = firstinvariant
  [../]
  [./si]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = secondinv
    scalar_type = secondinvariant
  [../]
  [./ti]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = thirdinv
    scalar_type = thirdinvariant
  [../]
  [./maxprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = maxprincipal
    scalar_type = MaxPRiNCIpAl
  [../]
  [./midprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = midprincipal
    scalar_type = MidPRiNCIpAl
  [../]
  [./minprincipal]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = minprincipal
    scalar_type = MiNPRiNCIpAl
  [../]
  [./direction]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = direction
    scalar_type = direction
    direction = '1 1 1'
  [../]
  [./max_shear]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = max_shear
    scalar_type = MaxShear
  [../]
  [./sint]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = sint
    scalar_type = StressIntensity
  [../]


[] # AuxKernels

[BCs]

  [./node1_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./node1_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1
    function = rampConstant2
  [../]
  [./node1_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 1
    function = rampConstant3
  [../]

  [./node2_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 2
    function = rampConstant1
  [../]
  [./node2_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 2
    function = rampConstant2
  [../]
  [./node2_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 2
    function = rampConstant6
  [../]

  [./node3_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 3
    function = rampConstant1
  [../]
  [./node3_y]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]
  [./node3_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 3
    function = rampConstant3
  [../]

  [./node4_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]
  [./node4_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  [../]
  [./node4_z]
    type = DirichletBC
    variable = disp_z
    boundary = 4
    value = 0.0
  [../]

  [./node5_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 5
    function = rampConstant1
  [../]
  [./node5_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = rampConstant4
  [../]
  [./node5_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 5
    function = rampConstant3
  [../]

  [./node6_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 6
    function = rampConstant2
  [../]
  [./node6_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 6
    function = rampConstant4
  [../]
  [./node6_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 6
    function = rampConstant6
  [../]

  [./node7_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 7
    function = rampConstant3
  [../]

  [./node8_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 8
    function = rampConstant1
  [../]
  [./node8_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 8
    function = rampConstant2
  [../]
  [./node8_z]
    type = DirichletBC
    variable = disp_z
    boundary = 8
    value = 0.0
  [../]


[] # BCs

[Materials]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.0
  [../]

  [./strain]
    type = ComputeFiniteStrain
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

[] # Materials

[Executioner]

  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-10

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 2
  end_time = 2.0
[] # Executioner

[Outputs]
  exodus = true
[] # Outputs