# Compute Cracked Stress

Computes energy and modifies the stress for phase field fracture

## Description

This material implements a phase field fracture model that can include anisotropic elasticity tensors, modifying the stress and computing the free energy derivatives required for the model. It works with the standard phase field kernels for nonconserved variables. In the model, a nonconserved order parameter defines the crack, where in undamaged material and in cracked material. Cracked material can sustain a compressive stress, but not a tensile one. evolves to minimize the elastic free energy of the system.

This model takes the stress and Jacobian_mult that were calculated by another material and modifies them to include cracks.

## Model Summary

In the model, the uncracked stress is provided by another material. It is decomposed into its compressive and tensile parts using a spectral decomposition (1) The compressive and tensile parts of the stress are computed from postive and negative projection tensors (computed from the spectral decomposition) according to (2) (3)

## Free Energy Calculation

The total strain energy density is defined as (4) where is the strain energy due to tensile stress, is the strain energy due to compressive stress, and is a parameter used to avoid non-positive definiteness at or near complete damage. The compressive and tensile strain energies are determined from: (5) (6)

The crack energy density is defined as (7) where is the width of the crack interface and is a parameter related to the energy release rate.

The total local free energy density is defined as (8)

## Stress Definition

To be thermodynamically consistent, the stress is related to the deformation energy density according to (9) Since (10) (11) then, (12)

The Jacobian matrix for the stress is (13) where is the Jacobian_mult that was calculated by the constitutive model.

## Evolution Equation and History Variable

To avoid crack healing, a history variable is defined that is the maximum energy density over the time interval , where is the current time step, i.e. (14)

Now, the total free energy is redefined as: (15) with (16) Its derivatives are (17)

The evolution equation for the damage parameter follows the Allen-Cahn equation (18) where and .

This equation follows the standard Allen-Cahn and thus can be implemented in MOOSE using the standard Allen-Cahn kernels, TimeDerivative, AllenCahn, and ACInterface. There is now an action that automatically generates these kernels: NonconservedAction. See the PhaseField module documentation for more information.

## Example Input File Syntax


[./cracked_stress]
type = ComputeCrackedStress
c = c
kdamage = 1e-6
F_name = E_el
use_current_history_variable = true
uncracked_base_name = uncracked
[../]
(moose/modules/combined/test/tests/phase_field_fracture/crack2d_computeCrackedStress_smallstrain.i)

## Input Parameters

• cOrder parameter for damage

C++ Type:std::vector

Description:Order parameter for damage

• uncracked_base_nameThe base name used to calculate the original stress

C++ Type:std::string

Description:The base name used to calculate the original stress

### Required Parameters

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• base_nameThe base name used to save the cracked stress

C++ Type:std::string

Description:The base name used to save the cracked stress

• F_nameE_elName of material property storing the elastic energy

Default:E_el

C++ Type:MaterialPropertyName

Description:Name of material property storing the elastic energy

• kappa_namekappa_opName of material property being created to store the interfacial parameter kappa

Default:kappa_op

C++ Type:MaterialPropertyName

Description:Name of material property being created to store the interfacial parameter kappa

• finite_strain_modelFalseThe model is using finite strain

Default:False

C++ Type:bool

Description:The model is using finite strain

• kdamage1e-09Stiffness of damaged matrix

Default:1e-09

C++ Type:double

Description:Stiffness of damaged matrix

• use_current_history_variableFalseUse the current value of the history variable.

Default:False

C++ Type:bool

Description:Use the current value of the history variable.

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• mobility_nameLName of material property being created to store the mobility L

Default:L

C++ Type:MaterialPropertyName

Description:Name of material property being created to store the mobility L

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• 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

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.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• 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 computeSubdomainProperties() 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

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 computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object