Compute Smeared Cracking Stress

Compute stress using a fixed smeared cracking model

Description

This class implements a fixed smeared cracking model, which represents cracking as a softening stress-strain law at the material points as opposed to introducing topographic changes to the mesh, as would be the case with a discrete cracking model.

In this model, principal stresses are compared to a critical stress. If one of the principal stresses exceeds the critical stress, the material point is considered cracked in that direction, and the model transitions to an orthotropic model, in which the stress in the cracked direction is decreased according to a softening law. Material behavior in the cracking direction is affected in two ways: reduction of the stiffness in that direction, and adjusting the stress to follow the softening curve.

Interaction with Inelastic Models

This class derives from ComputeMultipleInelasticStrain, and prior to cracking, allows multiple inelastic models to be active. Once cracking occurs, the inelastic strains at that material point are preserved, but those models are no longer called for the duration of the simulation, and inelastic strains from those other models are no longer permitted to evolve.

Cracking Direction Determination

The orientation of the principal coordinate system is determined from the eigenvectors of the elastic strain tensor. However, once a crack direction is determined, that direction remains fixed and further cracks are considered in directions perpendicular to the original crack direction. Note that for axisymmetric problems, one crack direction is known a priori. The theta or out-of-plane direction is not coupled to the $var element = document.getElementById("moose-equation-a1845d42-a366-427e-8d4d-f73add2152f4");katex.render("r", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-49d19862-bf57-4ade-ac75-1700ae5fe9c2");katex.render("z", element, {displayMode:false,throwOnError:false});$ directions (i.e., no $var element = document.getElementById("moose-equation-4b774684-0f2b-44ad-b343-614b25fedcc1");katex.render("r\\theta", element, {displayMode:false,throwOnError:false});$ or $var element = document.getElementById("moose-equation-086e24b1-ba4f-4ec6-a235-844bca88d93d");katex.render("z\\theta", element, {displayMode:false,throwOnError:false});$ shear strain/stress exists) and is therefore a known or principal direction.

If we store a scalar value, $var element = document.getElementById("moose-equation-1039cdc8-aa89-44c8-bb69-8dbbbab3a359");katex.render("c_i", element, {displayMode:false,throwOnError:false});$ , for each of the three possible crack directions at a material point, these in combination with the principal directions (eigenvectors or rotation tensor) provide a convenient way to eliminate stress in cracked directions. A value of 1 for $var element = document.getElementById("moose-equation-0d114083-a4ae-4ab8-ac43-40fe8143e21c");katex.render("c_i", element, {displayMode:false,throwOnError:false});$ indicates that the material point has not cracked in that direction. A value very close to zero (not zero for numerical reasons) indicates that cracking has occurred.

We define a cracking tensor in the cracked orientation as $var element = document.getElementById("moose-equation-75dc6ca3-53ef-45b5-a212-0f4b487cbf6f");katex.render("\\boldsymbol{c}", element, {displayMode:false,throwOnError:false});$ : $var element = document.getElementById("moose-equation-c0d69981-9c05-42e8-8cfa-86dac789c59a");katex.render("\\boldsymbol{c}= \\begin{bmatrix} c_1 & & \\\\ & c_2 & \\\\ & & c_3 \\end{bmatrix}.", element, {displayMode:true,throwOnError:false});$ The rotation tensor $var element = document.getElementById("moose-equation-efc07fa2-e432-41e4-994f-aefb7456abb1");katex.render("\\boldsymbol{R}", element, {displayMode:false,throwOnError:false});$ is defined in terms of the eigenvectors $var element = document.getElementById("moose-equation-11f62b75-d181-4919-b67c-ff65c2590e0b");katex.render("e_i", element, {displayMode:false,throwOnError:false});$ : $var element = document.getElementById("moose-equation-914a1f4d-0cae-4f10-a375-24be3520df83");katex.render("\\boldsymbol{R}= \\begin{bmatrix} e_1 & e_2 & & e_3 \\end{bmatrix}.", element, {displayMode:true,throwOnError:false});$ This leads to a transformation operator $var element = document.getElementById("moose-equation-41a9f0d0-80e7-4c56-9c2a-e8d78fefdea2");katex.render("\\boldsymbol{T}", element, {displayMode:false,throwOnError:false});$ : $var element = document.getElementById("moose-equation-73ee5e67-6c5c-4c7c-ad65-e66fa777a505");katex.render("\\boldsymbol{T}=\\boldsymbol{R}\\boldsymbol{c}\\boldsymbol{R}^T.", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-c8c3acd8-db3c-4e9a-9562-01222e3237e4");katex.render("\\boldsymbol{T}", element, {displayMode:false,throwOnError:false});$ is useful for transforming uncracked tensors in the global frame to cracked tensors in the same frame. For example, the cracked stress $var element = document.getElementById("moose-equation-e0fb0919-14fa-4845-987d-ff7b6343b0a1");katex.render("\\boldsymbol{\\sigma}_{cg}", element, {displayMode:false,throwOnError:false});$ in terms of the stress $var element = document.getElementById("moose-equation-aed58231-e883-4dda-a29d-4d307e5d0630");katex.render("\\boldsymbol{\\sigma}_g", element, {displayMode:false,throwOnError:false});$ is (subscript $var element = document.getElementById("moose-equation-7f1d99c8-bef3-4a9b-9dff-ae73569cde58");katex.render("c", element, {displayMode:false,throwOnError:false});$ indicates cracked, $var element = document.getElementById("moose-equation-e83ef583-10ab-49bf-9894-7bc4b71d143b");katex.render("l", element, {displayMode:false,throwOnError:false});$ local frame, and $var element = document.getElementById("moose-equation-a6422728-33d4-4986-9371-ccd6d561a06e");katex.render("g", element, {displayMode:false,throwOnError:false});$ global frame): $var element = document.getElementById("moose-equation-14dfa154-3161-4322-adb4-bc54311b69dc");katex.render("\\begin{aligned} \\boldsymbol{\\sigma}_{cg} & = \\boldsymbol{T}\\boldsymbol{\\sigma}_g\\boldsymbol{T}^T \\\\ & = \\boldsymbol{RcR}^T\\boldsymbol{\\sigma}_g\\boldsymbol{RcR}^T \\\\ & = \\boldsymbol{Rc}\\boldsymbol{\\sigma}_l\\boldsymbol{cR}^T \\\\ & = \\boldsymbol{R}\\boldsymbol{\\sigma}_{cl}\\boldsymbol{R}^T. \\end{aligned}", element, {displayMode:true,throwOnError:false});$

When many material points have multiple cracks, the solution becomes difficult to obtain numerically. For this reason, controls are available to limit the number and direction of cracks that are allowed. Also, there are options to control the amount of shear retention and amount of stress correction during softening, both of which can significantly affect convergence.

Example Input File Syntax

[./elastic_stress]
  type = ComputeSmearedCrackingStress
  cracking_stress = 1.68e6
  softening_models = abrupt_softening
[../]

Input Parameters

cracking_stressThe stress threshold beyond which cracking occurs. Negative values prevent cracking.
C++ Type:std::vector<VariableName>
Controllable:No
Description:The stress threshold beyond which cracking occurs. Negative values prevent cracking.
inelastic_modelsThe material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.
C++ Type:std::vector<MaterialName>
Controllable:No
Description:The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.

Required Parameters

absolute_tolerance1e-05Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called
Default:1e-05
C++ Type:double
Controllable:No
Description:Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called
base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
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
combined_inelastic_strain_weightsThe combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1
C++ Type:std::vector<double>
Controllable:No
Description:The combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1
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_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
cracking_neg_fraction0The fraction of the cracking strain at which a transition begins during decreasing strain to the original stiffness.
Default:0
C++ Type:double
Controllable:No
Description:The fraction of the cracking strain at which a transition begins during decreasing strain to the original stiffness.
cycle_modelsFalseAt timestep N use only inelastic model N % num_models.
Default:False
C++ Type:bool
Controllable:No
Description:At timestep N use only inelastic model N % num_models.
damage_modelName of the damage model
C++ Type:MaterialName
Controllable:No
Description:Name of the damage model
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.
internal_solve_full_iteration_historyFalseSet to true to output stress update iteration information over the stress change
Default:False
C++ Type:bool
Controllable:No
Description:Set to true to output stress update iteration information over the stress change
max_cracks3The maximum number of cracks allowed at a material point.
Default:3
C++ Type:unsigned int
Controllable:No
Description:The maximum number of cracks allowed at a material point.
max_iterations30Maximum number of the stress update iterations over the stress change after all update materials are called
Default:30
C++ Type:unsigned int
Controllable:No
Description:Maximum number of the stress update iterations over the stress change after all update materials are called
max_stress_correction1Maximum permitted correction to the predicted stress as a ratio of the stress change to the predicted stress from the previous step's damage level. Values less than 1 will improve robustness, but not be as accurate.
Default:1
C++ Type:double
Controllable:No
Description:Maximum permitted correction to the predicted stress as a ratio of the stress change to the predicted stress from the previous step's damage level. Values less than 1 will improve robustness, but not be as accurate.
perform_finite_strain_rotationsTrueTensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains
Default:True
C++ Type:bool
Controllable:No
Description:Tensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains
prescribed_crack_directionsPrescribed directions of first cracks
C++ Type:MultiMooseEnum
Options:x, y, z
Controllable:No
Description:Prescribed directions of first cracks
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.
relative_tolerance1e-05Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called
Default:1e-05
C++ Type:double
Controllable:No
Description:Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called
shear_retention_factor0Fraction of original shear stiffness to be retained after cracking
Default:0
C++ Type:double
Controllable:No
Description:Fraction of original shear stiffness to be retained after cracking
softening_modelsThe material objects used to compute softening behavior for loading a crack.Either 1 or 3 models must be specified. If a single model is specified, it isused for all directions. If 3 models are specified, they will be used for the3 crack directions in sequence
C++ Type:std::vector<MaterialName>
Controllable:No
Description:The material objects used to compute softening behavior for loading a crack.Either 1 or 3 models must be specified. If a single model is specified, it isused for all directions. If 3 models are specified, they will be used for the3 crack directions in sequence
tangent_operatornonlinearType of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.
Default:nonlinear
C++ Type:MooseEnum
Options:elastic, nonlinear
Controllable:No
Description:Type of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.

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

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

(moose/modules/tensor_mechanics/test/tests/smeared_cracking/cracking.i)

#
# Simple pull test for cracking.
# The stress increases for two steps and then drops to zero.

[Mesh]
  file = cracking_test.e
[]

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

[Functions]
  [./displ]
    type = PiecewiseLinear
    x = '0 1 2 3  4'
    y = '0 1 0 -1 0'
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    add_variables = true
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
  [../]
[]

[BCs]
  [./pull]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 4
    function = displ
  [../]
  [./left]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  [../]
  [./back]
    type = DirichletBC
    variable = disp_z
    boundary = 3
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.8e7
    poissons_ratio = 0
  [../]
  [./elastic_stress]
    type = ComputeSmearedCrackingStress
    cracking_stress = 1.68e6
    softening_models = abrupt_softening
  [../]
  [./abrupt_softening]
    type = AbruptSoftening
  [../]
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -sub_pc_type'
  petsc_options_value = '101                asm      lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  l_tol = 1e-5
  start_time = 0.0
  end_time = 0.1
  dt = 0.025
[]

[Outputs]
  exodus = true
[]