CrystalPlasticityTwinningKalidindiUpdate

Twinning propagation model based on Kalidindi's treatment of twinning in a FCC material

CrystalPlasticityTwinningKalidindiUpdate is designed to be used in conjunction with the ComputeMultipleCrystalPlasticityStress class to calculate the response of a FCC crystalline solid. Details about the algorithm and specific stress and strain measures used in the CrystalPlasticityUpdate base class are given on the documentation page for ComputeMultipleCrystalPlasticityStress.

Additionally CrystalPlasticityTwinningKalidindiUpdate is intended to be used with a constitutive model for dislocation glide or slip: combining this twinning model with CrystalPlasticityKalidindiUpdate will replicate the coupling of the two constitutive models through the plastic velocity gradient calcualtion as presented in Kalidindi (2001).

Constitutive Model Definition

Proposed by Kalidindi, this straight-forward twinning propagation model computes the plastic shear increment due to twinning with a power law constiutive model: $var element = document.getElementById("moose-equation-1bb05bcd-dc78-4597-a170-b2d0cc0a6661");katex.render(" \\Delta \\gamma^{\\beta} = \\gamma_o \\left| \\frac{\\tau^{\\beta}}{g^{\\beta}} \\right|^{1/m} \\quad if \\quad \\tau^{\\beta} > 0, \\quad f_{total} < f_{limit}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-2ac2549e-9e8b-4679-bd09-2a1686d2f498");katex.render("\\gamma_o", element, {displayMode:false,throwOnError:false});$ is the reference slip rate, $var element = document.getElementById("moose-equation-8db4190b-98e9-4053-8ab3-edf05553eeb1");katex.render("\\tau^{\\beta}", element, {displayMode:false,throwOnError:false});$ is the applied resolved shear stress, g $var element = document.getElementById("moose-equation-3ebcaf7e-94bb-4e3c-a17a-cca78041833d");katex.render("^{\\beta}", element, {displayMode:false,throwOnError:false});$ is the twin propagation resistance value, m is the slip rate sensitivity exponent, f $var element = document.getElementById("moose-equation-ca7343bb-2ce3-4dca-acbf-c3ed5c1f7abe");katex.render("_{total}", element, {displayMode:false,throwOnError:false});$ is the sum of the twin volume fraction on all twin systems, and f $var element = document.getElementById("moose-equation-24f9882d-8bad-409f-8399-bb3a403c0db2");katex.render("_{limit}", element, {displayMode:false,throwOnError:false});$ is the user-defined upper limit for the twin volume fraction. This constitutive model does not allow de-twinning.

The rate of twin volume fraction on each twin system is calculated from the system plastic shear increment $var element = document.getElementById("moose-equation-2da7b044-68f7-4385-8853-6cfecbd301e6");katex.render(" \\dot{f}^{\\beta} = \\frac{\\dot{\\gamma}^{\\beta}}{\\gamma_{tw}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4188c1c3-bf93-4578-b7b6-46fb30b193b2");katex.render("\\gamma_{tw}", element, {displayMode:false,throwOnError:false});$ is the characteristic shear of the twin (Kalidindi, 2001).

The twin propagation resistance is calculated as a function of the twin volume fraction and the characteristic twin shear, with different hardening coefficients for non-coplanar and coplanar twinning systems. The different coefficients are required to capture experimental observations of early twinning deformation on non-coplanar systems (Kalidindi, 2001). $var element = document.getElementById("moose-equation-9d859e33-0a2e-425d-9e35-7c9f66996903");katex.render("\\Delta g^{\\beta} = \\gamma_{tw} \\left[ h_{nc}\\left( f_{total} \\right)^b \\sum_{nc}^k \\dot{f}^k + h_{cp}\\left( f_{total} \\right) \\sum_{cp}^k \\dot{f}^k \\right]", element, {displayMode:true,throwOnError:false});$ where h $var element = document.getElementById("moose-equation-8b6631f7-c175-4b5c-a688-e8326d3f9008");katex.render("_{nc}", element, {displayMode:false,throwOnError:false});$ is the user-defined non-coplanar hardening coefficent, b is the hardening exponent for non-coplanar twin systems, and h $var element = document.getElementById("moose-equation-8cb75162-5f4d-42d0-8468-a0368fea4974");katex.render("_{cp}", element, {displayMode:false,throwOnError:false});$ is the user-defined coplanar hardening coefficient.

Plastic Velocity Gradient Calculation

In simulations where both twin propagation and dislocation slip constitutive models are included, the influence of the twin propagation on the plastic velocity gradient is implemented as a fraction of the twin volume fraction $(1)var element = document.getElementById("moose-equation-338088f3-92b6-442c-b642-d4600d27cfb4");katex.render(" L^P = \\left(1 - {f_{total}}_{(n-1)} \\right) \\sum_{\\alpha}^{slip} \\dot{\\gamma}^{\\alpha} S^{\\alpha}_o + \\sum_{\\beta}^{twin} \\dot{f}^{\\beta}\\gamma_{tw}S^{\\beta}_o", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-af44f95e-0fca-4a10-832b-9f1331c3b44e");katex.render("\\dot{\\gamma}^{\\alpha}", element, {displayMode:false,throwOnError:false});$ is the plastic shear rate due to dislocation slip, S $var element = document.getElementById("moose-equation-07d0e845-6d54-4d49-a158-80c5768d7f33");katex.render("^{\\alpha}_o", element, {displayMode:false,throwOnError:false});$ is the Schmid tensor for the slip systems, and S $var element = document.getElementById("moose-equation-84797547-3f31-4e76-adf7-17a0d5fb34a6");katex.render("^{\\beta}_o", element, {displayMode:false,throwOnError:false});$ is the Schmid tensor for the twinning system. Note that the value of the total volume fraction of twins used in Eq. (1) lags by single timestep. The use of this lagged value is designated by the $var element = document.getElementById("moose-equation-9af99d25-586b-413b-acb9-c0476f164ca4");katex.render("(n-1)", element, {displayMode:false,throwOnError:false});$ subscript. This modification requires that the name for the total twin volume fraction material property be provided to the dislocation slip constitutive model as shown below.

Example Input File Syntax

[twin_only_xtalpl]
  type = CrystalPlasticityTwinningKalidindiUpdate
  number_slip_systems = 12
  slip_sys_file_name = 'fcc_input_twinning_systems.txt'
  initial_twin_lattice_friction = 3.0
  non_coplanar_coefficient_twin_hardening = 8e5
  coplanar_coefficient_twin_hardening = 8e4
[]

CrystalPlasticityTwinningKalidindiUpdate must be run in conjunction with the crystal plasticity specific stress calculator as shown below:

[stress]
  type = ComputeMultipleCrystalPlasticityStress
  crystal_plasticity_models = 'twin_only_xtalpl'
  tan_mod_type = exact
  maximum_substep_iteration = 2
[]

In most cases this twinning model is intended to be used with a dislocation glide or slip model, such as CrystalPlasticityKalidindiUpdate. To couple the volume fraction of twins to the dislocation slip plastic velocity gradient contribution, as shown in Eq. (1). The name of the total twin volume fraction material property must be supplied to the glide or slip material model:

[slip_xtalpl]
  type = CrystalPlasticityKalidindiUpdate
  number_slip_systems = 12
  slip_sys_file_name = input_slip_sys.txt
  total_twin_volume_fraction = 'twin_total_volume_fraction_twins'
[]

Input Parameters

number_slip_systemsThe total number of possible active slip systems for the crystalline material
C++ Type:unsigned int
Controllable:No
Description:The total number of possible active slip systems for the crystalline material
slip_sys_file_nameName of the file containing the slip systems, one slip system per row, with the slip plane normal given before the slip plane direction.
C++ Type:FileName
Controllable:No
Description:Name of the file containing the slip systems, one slip system per row, with the slip plane normal given before the slip plane direction.

Required Parameters

base_nameOptional parameter that allows the user to define multiple crystal plasticity mechanisms
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple crystal plasticity mechanisms
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
characteristic_twin_shear0.707107The amount of shear that is associated with a twin in this cubic structure
Default:0.707107
C++ Type:double
Controllable:No
Description:The amount of shear that is associated with a twin in this cubic structure
constant_onNONEWhen 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:NONE
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
coplanar_coefficient_twin_hardening800Hardening coefficient for coplanar twin systems strength as a function of the volume fraction of twins
Default:800
C++ Type:double
Controllable:No
Description:Hardening coefficient for coplanar twin systems strength as a function of the volume fraction of twins
crystal_lattice_typeFCCCrystal lattice type or representative unit cell, i.e., BCC, FCC, HCP, etc.
Default:FCC
C++ Type:MooseEnum
Options:BCC, FCC, HCP
Controllable:No
Description:Crystal lattice type or representative unit cell, i.e., BCC, FCC, HCP, etc.
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
initial_total_twin_volume_fraction0The initial sum of the twin volume fraction across all twin systems in the crystal, if any. This value is distributed evenly across all twin systems in the crystal.
Default:0
C++ Type:double
Controllable:No
Description:The initial sum of the twin volume fraction across all twin systems in the crystal, if any. This value is distributed evenly across all twin systems in the crystal.
initial_twin_lattice_friction0The initial value of the lattice friction for twin propogation, often calculated as a fraction of the Peierls strength
Default:0
C++ Type:double
Controllable:No
Description:The initial value of the lattice friction for twin propogation, often calculated as a fraction of the Peierls strength
non_coplanar_coefficient_twin_hardening8000The factor to apply to the hardening of non-coplanar twin systems strength as a function of the volume fraction of twins
Default:8000
C++ Type:double
Controllable:No
Description:The factor to apply to the hardening of non-coplanar twin systems strength as a function of the volume fraction of twins
non_coplanar_twin_hardening_exponent0.05Parameter used to increase the hardening of non-coplanar twin systems such that the propagation of twins on conplanar systems is favored at early deformation stages.
Default:0.05
C++ Type:double
Controllable:No
Description:Parameter used to increase the hardening of non-coplanar twin systems such that the propagation of twins on conplanar systems is favored at early deformation stages.
number_cross_slip_directions0Quanity of unique slip directions, used to determine cross slip familes
Default:0
C++ Type:double
Controllable:No
Description:Quanity of unique slip directions, used to determine cross slip familes
number_cross_slip_planes0Quanity of slip planes belonging to a single cross slip direction; used to determine cross slip families
Default:0
C++ Type:double
Controllable:No
Description:Quanity of slip planes belonging to a single cross slip direction; used to determine cross slip families
print_state_variable_convergence_error_messagesFalseWhether or not to print warning messages from the crystal plasticity specific convergence checks on both the constiutive model internal state variables.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to print warning messages from the crystal plasticity specific convergence checks on both the constiutive model internal state variables.
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.
resistance_tol0.01Constitutive slip system resistance relative residual tolerance for each individual constitutive model
Default:0.01
C++ Type:double
Controllable:No
Description:Constitutive slip system resistance relative residual tolerance for each individual constitutive model
slip_increment_tolerance0.02Maximum allowable slip in an increment for each individual constitutive model
Default:0.02
C++ Type:double
Controllable:No
Description:Maximum allowable slip in an increment for each individual constitutive model
stol0.01Constitutive internal state variable relative change tolerance
Default:0.01
C++ Type:double
Controllable:No
Description:Constitutive internal state variable relative change tolerance
twin_reference_strain_rate0.001The reference strain rate, gamma_o, for the power law plastic slip law due to twin propagation.
Default:0.001
C++ Type:double
Controllable:No
Description:The reference strain rate, gamma_o, for the power law plastic slip law due to twin propagation.
twin_strain_rate_sensitivity_exponent0.05The strain rate sensitivity exponent for twin propagation power law strain rate calculation
Default:0.05
C++ Type:double
Controllable:No
Description:The strain rate sensitivity exponent for twin propagation power law strain rate calculation
unit_cell_dimension1 1 1 The dimension of the unit cell along three directions, where a cubic unit cell is assumed for cubic crystals and a hexagonal unit cell (a, a, c) is assumed for HCP crystals. These dimensions will be taken into account while computing the slip systems. Default size is 1.0 along all three directions.
Default:1 1 1
C++ Type:std::vector<double>
Controllable:No
Description:The dimension of the unit cell along three directions, where a cubic unit cell is assumed for cubic crystals and a hexagonal unit cell (a, a, c) is assumed for HCP crystals. These dimensions will be taken into account while computing the slip systems. Default size is 1.0 along all three directions.
upper_limit_twin_volume_fraction0.8The maximumum amount of twinning volume fraction allowed
Default:0.8
C++ Type:double
Controllable:No
Description:The maximumum amount of twinning volume fraction allowed
zero_tol1e-12Tolerance for residual check when variable value is zero for each individual constitutive model
Default:1e-12
C++ Type:double
Controllable:No
Description:Tolerance for residual check when variable value is zero for each individual constitutive model

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

References

Surya R Kalidindi. Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals. International Journal of Plasticity, 17:837–860, 2001.

@article{kalidindi2001,
    author = "Kalidindi, Surya R",
    title = "Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals",
    journal = "International Journal of Plasticity",
    volume = "17",
    pages = "837--860",
    year = "2001",
    publisher = "Elsevier"
}

(moose/modules/tensor_mechanics/test/tests/crystal_plasticity/twinning/only_twinning_fcc.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 2
    elem_type = HEX8
  []
[]

[AuxVariables]
  [fp_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_twin_volume_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_resistance_4]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_resistance_10]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_volume_fraction_0]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_1]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_2]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_3]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_4]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_5]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_6]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_7]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_8]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_9]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_10]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_11]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_tau_4]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_tau_10]
   order = CONSTANT
   family = MONOMIAL
  []
[]

[Modules/TensorMechanics/Master/all]
  strain = FINITE
  add_variables = true
[]

[AuxKernels]
  [fp_zz]
    type = RankTwoAux
    variable = fp_zz
    rank_two_tensor = plastic_deformation_gradient
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  []
  [total_twin_volume_fraction]
    type = MaterialRealAux
    variable = total_twin_volume_fraction
    property = total_volume_fraction_twins
    execute_on = timestep_end
  []
  [twin_resistance_4]
   type = MaterialStdVectorAux
   variable = twin_resistance_4
   property = slip_resistance
   index = 4
   execute_on = timestep_end
  []
  [twin_resistance_10]
   type = MaterialStdVectorAux
   variable = twin_resistance_10
   property = slip_resistance
   index = 10
   execute_on = timestep_end
  []
  [twin_volume_fraction_0]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_0
   property = twin_system_volume_fraction
   index = 0
   execute_on = timestep_end
  []
  [twin_volume_fraction_1]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_1
   property = twin_system_volume_fraction
   index = 1
   execute_on = timestep_end
  []
  [twin_volume_fraction_2]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_2
   property = twin_system_volume_fraction
   index = 2
   execute_on = timestep_end
  []
  [twin_volume_fraction_3]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_3
   property = twin_system_volume_fraction
   index = 3
   execute_on = timestep_end
  []
  [twin_volume_fraction_4]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_4
   property = twin_system_volume_fraction
   index = 4
   execute_on = timestep_end
  []
  [twin_volume_fraction_5]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_5
   property = twin_system_volume_fraction
   index = 5
   execute_on = timestep_end
  []
  [twin_volume_fraction_6]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_6
   property = twin_system_volume_fraction
   index = 6
   execute_on = timestep_end
  []
  [twin_volume_fraction_7]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_7
   property = twin_system_volume_fraction
   index = 7
   execute_on = timestep_end
  []
  [twin_volume_fraction_8]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_8
   property = twin_system_volume_fraction
   index = 8
   execute_on = timestep_end
  []
  [twin_volume_fraction_9]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_9
   property = twin_system_volume_fraction
   index = 9
   execute_on = timestep_end
  []
  [twin_volume_fraction_10]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_10
   property = twin_system_volume_fraction
   index = 10
   execute_on = timestep_end
  []
  [twin_volume_fraction_11]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_11
   property = twin_system_volume_fraction
   index = 11
   execute_on = timestep_end
  []
  [twin_tau_4]
    type = MaterialStdVectorAux
    variable = twin_tau_4
    property = applied_shear_stress
    index = 4
    execute_on = timestep_end
  []
  [twin_tau_10]
    type = MaterialStdVectorAux
    variable = twin_tau_10
    property = applied_shear_stress
    index = 10
    execute_on = timestep_end
  []
[]

[BCs]
  [fix_y]
    type = DirichletBC
    variable = disp_y
    preset = true
    boundary = 'bottom'
    value = 0
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0
  []
  [tdisp]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = '5.0e-4*t'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeElasticityTensorCP
    C_ijkl = '1.08e5 6.034e4 6.034e4 1.08e5 6.03e4 1.08e5 2.86e4 2.86e4 2.86e4' #Tallon and Wolfenden. J. Phys. Chem. Solids (1979)
    fill_method = symmetric9
    euler_angle_1 = 54.74
    euler_angle_2 = 45.0
    euler_angle_3 = 270.0
  []
  [stress]
    type = ComputeMultipleCrystalPlasticityStress
    crystal_plasticity_models = 'twin_only_xtalpl'
    tan_mod_type = exact
    maximum_substep_iteration = 2
  []
  [twin_only_xtalpl]
    type = CrystalPlasticityTwinningKalidindiUpdate
    number_slip_systems = 12
    slip_sys_file_name = 'fcc_input_twinning_systems.txt'
    initial_twin_lattice_friction = 3.0
    non_coplanar_coefficient_twin_hardening = 8e5
    coplanar_coefficient_twin_hardening = 8e4
  []
[]

[Postprocessors]
  [fp_zz]
    type = ElementAverageValue
    variable = fp_zz
  []
  [total_twin_volume_fraction]
    type = ElementAverageValue
    variable = total_twin_volume_fraction
  []
  [twin_resistance_4]
    type = ElementAverageValue
    variable = twin_resistance_4
  []
  [twin_resistance_10]
    type = ElementAverageValue
    variable = twin_resistance_10
  []
  [twin_volume_fraction_0]
    type = ElementAverageValue
    variable = twin_volume_fraction_0
  []
  [twin_volume_fraction_1]
    type = ElementAverageValue
    variable = twin_volume_fraction_1
  []
  [twin_volume_fraction_2]
    type = ElementAverageValue
    variable = twin_volume_fraction_2
  []
  [twin_volume_fraction_3]
    type = ElementAverageValue
    variable = twin_volume_fraction_3
  []
  [twin_volume_fraction_4]
    type = ElementAverageValue
    variable = twin_volume_fraction_4
  []
  [twin_volume_fraction_5]
    type = ElementAverageValue
    variable = twin_volume_fraction_5
  []
  [twin_volume_fraction_6]
    type = ElementAverageValue
    variable = twin_volume_fraction_6
  []
  [twin_volume_fraction_7]
    type = ElementAverageValue
    variable = twin_volume_fraction_7
  []
  [twin_volume_fraction_8]
    type = ElementAverageValue
    variable = twin_volume_fraction_8
  []
  [twin_volume_fraction_9]
    type = ElementAverageValue
    variable = twin_volume_fraction_9
  []
  [twin_volume_fraction_10]
    type = ElementAverageValue
    variable = twin_volume_fraction_10
  []
  [twin_volume_fraction_11]
    type = ElementAverageValue
    variable = twin_volume_fraction_11
  []
  [twin_tau_4]
    type = ElementAverageValue
    variable = twin_tau_4
  []
  [twin_tau_10]
    type = ElementAverageValue
    variable = twin_tau_10
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  petsc_options_value = ' asm      2              lu            gmres     200'
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10
  nl_abs_step_tol = 1e-10

  dt = 0.025
  dtmin = 0.0125
  num_steps = 8
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(moose/modules/tensor_mechanics/test/tests/crystal_plasticity/twinning/only_twinning_fcc.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 2
    elem_type = HEX8
  []
[]

[AuxVariables]
  [fp_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_twin_volume_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_resistance_4]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_resistance_10]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_volume_fraction_0]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_1]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_2]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_3]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_4]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_5]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_6]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_7]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_8]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_9]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_10]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_11]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_tau_4]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_tau_10]
   order = CONSTANT
   family = MONOMIAL
  []
[]

[Modules/TensorMechanics/Master/all]
  strain = FINITE
  add_variables = true
[]

[AuxKernels]
  [fp_zz]
    type = RankTwoAux
    variable = fp_zz
    rank_two_tensor = plastic_deformation_gradient
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  []
  [total_twin_volume_fraction]
    type = MaterialRealAux
    variable = total_twin_volume_fraction
    property = total_volume_fraction_twins
    execute_on = timestep_end
  []
  [twin_resistance_4]
   type = MaterialStdVectorAux
   variable = twin_resistance_4
   property = slip_resistance
   index = 4
   execute_on = timestep_end
  []
  [twin_resistance_10]
   type = MaterialStdVectorAux
   variable = twin_resistance_10
   property = slip_resistance
   index = 10
   execute_on = timestep_end
  []
  [twin_volume_fraction_0]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_0
   property = twin_system_volume_fraction
   index = 0
   execute_on = timestep_end
  []
  [twin_volume_fraction_1]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_1
   property = twin_system_volume_fraction
   index = 1
   execute_on = timestep_end
  []
  [twin_volume_fraction_2]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_2
   property = twin_system_volume_fraction
   index = 2
   execute_on = timestep_end
  []
  [twin_volume_fraction_3]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_3
   property = twin_system_volume_fraction
   index = 3
   execute_on = timestep_end
  []
  [twin_volume_fraction_4]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_4
   property = twin_system_volume_fraction
   index = 4
   execute_on = timestep_end
  []
  [twin_volume_fraction_5]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_5
   property = twin_system_volume_fraction
   index = 5
   execute_on = timestep_end
  []
  [twin_volume_fraction_6]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_6
   property = twin_system_volume_fraction
   index = 6
   execute_on = timestep_end
  []
  [twin_volume_fraction_7]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_7
   property = twin_system_volume_fraction
   index = 7
   execute_on = timestep_end
  []
  [twin_volume_fraction_8]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_8
   property = twin_system_volume_fraction
   index = 8
   execute_on = timestep_end
  []
  [twin_volume_fraction_9]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_9
   property = twin_system_volume_fraction
   index = 9
   execute_on = timestep_end
  []
  [twin_volume_fraction_10]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_10
   property = twin_system_volume_fraction
   index = 10
   execute_on = timestep_end
  []
  [twin_volume_fraction_11]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_11
   property = twin_system_volume_fraction
   index = 11
   execute_on = timestep_end
  []
  [twin_tau_4]
    type = MaterialStdVectorAux
    variable = twin_tau_4
    property = applied_shear_stress
    index = 4
    execute_on = timestep_end
  []
  [twin_tau_10]
    type = MaterialStdVectorAux
    variable = twin_tau_10
    property = applied_shear_stress
    index = 10
    execute_on = timestep_end
  []
[]

[BCs]
  [fix_y]
    type = DirichletBC
    variable = disp_y
    preset = true
    boundary = 'bottom'
    value = 0
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0
  []
  [tdisp]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = '5.0e-4*t'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeElasticityTensorCP
    C_ijkl = '1.08e5 6.034e4 6.034e4 1.08e5 6.03e4 1.08e5 2.86e4 2.86e4 2.86e4' #Tallon and Wolfenden. J. Phys. Chem. Solids (1979)
    fill_method = symmetric9
    euler_angle_1 = 54.74
    euler_angle_2 = 45.0
    euler_angle_3 = 270.0
  []
  [stress]
    type = ComputeMultipleCrystalPlasticityStress
    crystal_plasticity_models = 'twin_only_xtalpl'
    tan_mod_type = exact
    maximum_substep_iteration = 2
  []
  [twin_only_xtalpl]
    type = CrystalPlasticityTwinningKalidindiUpdate
    number_slip_systems = 12
    slip_sys_file_name = 'fcc_input_twinning_systems.txt'
    initial_twin_lattice_friction = 3.0
    non_coplanar_coefficient_twin_hardening = 8e5
    coplanar_coefficient_twin_hardening = 8e4
  []
[]

[Postprocessors]
  [fp_zz]
    type = ElementAverageValue
    variable = fp_zz
  []
  [total_twin_volume_fraction]
    type = ElementAverageValue
    variable = total_twin_volume_fraction
  []
  [twin_resistance_4]
    type = ElementAverageValue
    variable = twin_resistance_4
  []
  [twin_resistance_10]
    type = ElementAverageValue
    variable = twin_resistance_10
  []
  [twin_volume_fraction_0]
    type = ElementAverageValue
    variable = twin_volume_fraction_0
  []
  [twin_volume_fraction_1]
    type = ElementAverageValue
    variable = twin_volume_fraction_1
  []
  [twin_volume_fraction_2]
    type = ElementAverageValue
    variable = twin_volume_fraction_2
  []
  [twin_volume_fraction_3]
    type = ElementAverageValue
    variable = twin_volume_fraction_3
  []
  [twin_volume_fraction_4]
    type = ElementAverageValue
    variable = twin_volume_fraction_4
  []
  [twin_volume_fraction_5]
    type = ElementAverageValue
    variable = twin_volume_fraction_5
  []
  [twin_volume_fraction_6]
    type = ElementAverageValue
    variable = twin_volume_fraction_6
  []
  [twin_volume_fraction_7]
    type = ElementAverageValue
    variable = twin_volume_fraction_7
  []
  [twin_volume_fraction_8]
    type = ElementAverageValue
    variable = twin_volume_fraction_8
  []
  [twin_volume_fraction_9]
    type = ElementAverageValue
    variable = twin_volume_fraction_9
  []
  [twin_volume_fraction_10]
    type = ElementAverageValue
    variable = twin_volume_fraction_10
  []
  [twin_volume_fraction_11]
    type = ElementAverageValue
    variable = twin_volume_fraction_11
  []
  [twin_tau_4]
    type = ElementAverageValue
    variable = twin_tau_4
  []
  [twin_tau_10]
    type = ElementAverageValue
    variable = twin_tau_10
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  petsc_options_value = ' asm      2              lu            gmres     200'
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10
  nl_abs_step_tol = 1e-10

  dt = 0.025
  dtmin = 0.0125
  num_steps = 8
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(moose/modules/tensor_mechanics/test/tests/crystal_plasticity/twinning/combined_twinning_slip_100compression.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
    elem_type = HEX8
  []
[]

[AuxVariables]
  [fp_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_twin_volume_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_0]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_1]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_2]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_3]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_4]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_5]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_6]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_7]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_8]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_9]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_10]
    order = CONSTANT
    family = MONOMIAL
  []
  [slip_increment_11]
    order = CONSTANT
    family = MONOMIAL
  []
  [twin_volume_fraction_0]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_1]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_2]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_3]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_4]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_5]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_6]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_7]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_8]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_9]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_10]
   order = CONSTANT
   family = MONOMIAL
  []
  [twin_volume_fraction_11]
   order = CONSTANT
   family = MONOMIAL
  []
[]

[Modules/TensorMechanics/Master/all]
  strain = FINITE
  add_variables = true
[]

[AuxKernels]
  [fp_zz]
    type = RankTwoAux
    variable = fp_zz
    rank_two_tensor = plastic_deformation_gradient
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  []
  [total_twin_volume_fraction]
    type = MaterialRealAux
    variable = total_twin_volume_fraction
    property = twin_total_volume_fraction_twins
    execute_on = timestep_end
  []
  [slip_increment_0]
   type = MaterialStdVectorAux
   variable = slip_increment_0
   property = slip_increment
   index = 0
   execute_on = timestep_end
  []
  [slip_increment_1]
   type = MaterialStdVectorAux
   variable = slip_increment_1
   property = slip_increment
   index = 1
   execute_on = timestep_end
  []
  [slip_increment_2]
   type = MaterialStdVectorAux
   variable = slip_increment_2
   property = slip_increment
   index = 2
   execute_on = timestep_end
  []
  [slip_increment_3]
   type = MaterialStdVectorAux
   variable = slip_increment_3
   property = slip_increment
   index = 3
   execute_on = timestep_end
  []
  [slip_increment_4]
   type = MaterialStdVectorAux
   variable = slip_increment_4
   property = slip_increment
   index = 4
   execute_on = timestep_end
  []
  [slip_increment_5]
   type = MaterialStdVectorAux
   variable = slip_increment_5
   property = slip_increment
   index = 5
   execute_on = timestep_end
  []
  [slip_increment_6]
   type = MaterialStdVectorAux
   variable = slip_increment_6
   property = slip_increment
   index = 6
   execute_on = timestep_end
  []
  [slip_increment_7]
   type = MaterialStdVectorAux
   variable = slip_increment_7
   property = slip_increment
   index = 7
   execute_on = timestep_end
  []
  [slip_increment_8]
   type = MaterialStdVectorAux
   variable = slip_increment_8
   property = slip_increment
   index = 8
   execute_on = timestep_end
  []
  [slip_increment_9]
   type = MaterialStdVectorAux
   variable = slip_increment_9
   property = slip_increment
   index = 9
   execute_on = timestep_end
  []
  [slip_increment_10]
   type = MaterialStdVectorAux
   variable = slip_increment_10
   property = slip_increment
   index = 10
   execute_on = timestep_end
  []
  [slip_increment_11]
   type = MaterialStdVectorAux
   variable = slip_increment_11
   property = slip_increment
   index = 11
   execute_on = timestep_end
  []
  [twin_volume_fraction_0]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_0
   property = twin_twin_system_volume_fraction
   index = 0
   execute_on = timestep_end
  []
  [twin_volume_fraction_1]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_1
   property = twin_twin_system_volume_fraction
   index = 1
   execute_on = timestep_end
  []
  [twin_volume_fraction_2]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_2
   property = twin_twin_system_volume_fraction
   index = 2
   execute_on = timestep_end
  []
  [twin_volume_fraction_3]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_3
   property = twin_twin_system_volume_fraction
   index = 3
   execute_on = timestep_end
  []
  [twin_volume_fraction_4]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_4
   property = twin_twin_system_volume_fraction
   index = 4
   execute_on = timestep_end
  []
  [twin_volume_fraction_5]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_5
   property = twin_twin_system_volume_fraction
   index = 5
   execute_on = timestep_end
  []
  [twin_volume_fraction_6]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_6
   property = twin_twin_system_volume_fraction
   index = 6
   execute_on = timestep_end
  []
  [twin_volume_fraction_7]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_7
   property = twin_twin_system_volume_fraction
   index = 7
   execute_on = timestep_end
  []
  [twin_volume_fraction_8]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_8
   property = twin_twin_system_volume_fraction
   index = 8
   execute_on = timestep_end
  []
  [twin_volume_fraction_9]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_9
   property = twin_twin_system_volume_fraction
   index = 9
   execute_on = timestep_end
  []
  [twin_volume_fraction_10]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_10
   property = twin_twin_system_volume_fraction
   index = 10
   execute_on = timestep_end
  []
  [twin_volume_fraction_11]
   type = MaterialStdVectorAux
   variable = twin_volume_fraction_11
   property = twin_twin_system_volume_fraction
   index = 11
   execute_on = timestep_end
  []
[]

[BCs]
  [fix_y]
    type = DirichletBC
    variable = disp_y
    preset = true
    boundary = 'bottom'
    value = 0
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0
  []
  [tdisp]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = '-0.025*t'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeElasticityTensorCP
    C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 0.754e5 0.754e5 0.754e5' # roughly copper
    fill_method = symmetric9
  []
  [stress]
    type = ComputeMultipleCrystalPlasticityStress
    crystal_plasticity_models = 'twin_xtalpl slip_xtalpl'
    tan_mod_type = exact
  []
  [twin_xtalpl]
    type = CrystalPlasticityTwinningKalidindiUpdate
    base_name = twin
    number_slip_systems = 12
    slip_sys_file_name = 'fcc_input_twinning_systems.txt'
    initial_twin_lattice_friction = 60.0
  []
  [slip_xtalpl]
    type = CrystalPlasticityKalidindiUpdate
    number_slip_systems = 12
    slip_sys_file_name = input_slip_sys.txt
    total_twin_volume_fraction = 'twin_total_volume_fraction_twins'
  []
[]

[Postprocessors]
  [fp_zz]
    type = ElementAverageValue
    variable = fp_zz
  []
  [total_twin_volume_fraction]
    type = ElementAverageValue
    variable = total_twin_volume_fraction
  []
  [slip_increment_0]
    type = ElementAverageValue
    variable = slip_increment_0
  []
  [slip_increment_1]
    type = ElementAverageValue
    variable = slip_increment_1
  []
  [slip_increment_2]
    type = ElementAverageValue
    variable = slip_increment_2
  []
  [slip_increment_3]
    type = ElementAverageValue
    variable = slip_increment_3
  []
  [slip_increment_4]
    type = ElementAverageValue
    variable = slip_increment_4
  []
  [slip_increment_5]
    type = ElementAverageValue
    variable = slip_increment_5
  []
  [slip_increment_6]
    type = ElementAverageValue
    variable = slip_increment_6
  []
  [slip_increment_7]
    type = ElementAverageValue
    variable = slip_increment_7
  []
  [slip_increment_8]
    type = ElementAverageValue
    variable = slip_increment_8
  []
  [slip_increment_9]
    type = ElementAverageValue
    variable = slip_increment_9
  []
  [slip_increment_10]
    type = ElementAverageValue
    variable = slip_increment_10
  []
  [slip_increment_11]
    type = ElementAverageValue
    variable = slip_increment_11
  []
  [twin_volume_fraction_0]
    type = ElementAverageValue
    variable = twin_volume_fraction_0
  []
  [twin_volume_fraction_1]
    type = ElementAverageValue
    variable = twin_volume_fraction_1
  []
  [twin_volume_fraction_2]
    type = ElementAverageValue
    variable = twin_volume_fraction_2
  []
  [twin_volume_fraction_3]
    type = ElementAverageValue
    variable = twin_volume_fraction_3
  []
  [twin_volume_fraction_4]
    type = ElementAverageValue
    variable = twin_volume_fraction_4
  []
  [twin_volume_fraction_5]
    type = ElementAverageValue
    variable = twin_volume_fraction_5
  []
  [twin_volume_fraction_6]
    type = ElementAverageValue
    variable = twin_volume_fraction_6
  []
  [twin_volume_fraction_7]
    type = ElementAverageValue
    variable = twin_volume_fraction_7
  []
  [twin_volume_fraction_8]
    type = ElementAverageValue
    variable = twin_volume_fraction_8
  []
  [twin_volume_fraction_9]
    type = ElementAverageValue
    variable = twin_volume_fraction_9
  []
  [twin_volume_fraction_10]
    type = ElementAverageValue
    variable = twin_volume_fraction_10
  []
  [twin_volume_fraction_11]
    type = ElementAverageValue
    variable = twin_volume_fraction_11
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  petsc_options_value = ' asm      2              lu            gmres     200'
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10
  nl_abs_step_tol = 1e-10

  dt = 0.005
  dtmin = 0.01
  num_steps = 10
[]

[Outputs]
  csv = true
  perf_graph = true
[]