Compute Isotropic Linear Elastic Phase Field Fracture Stress

Computes the stress and free energy derivatives for the phase field fracture model, with linear isotropic elasticity

Description

This material implements the phase field fracture model from Chakraborty et al., calculating the stress and 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 assumes linear elastic mechanical deformation with an isotropic elasticity tensor, where and are the first and second Lamè constants.

Free Energy Definition

The total strain energy density is defined as (1) 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. (2) where is the th eigenvalue of the strain tensor and is an operator that provides the positive or negative part.

The crack energy density is defined as (3) 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 (4)

Stress Definition

To be thermodynamically consistent, the stress is related to the deformation energy density according to (5) Thus, (6) where is the th eigenvector. The stress becomes (7)

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. (8)

Now, the total free energy is redefined as: (9) with (10) Its derivatives are (11)

The evolution equation for the damage parameter follows the Allen-Cahn equation (12) 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

[./pf_elastic_energy]
  type = ComputeIsotropicLinearElasticPFFractureStress
  c = c
  F_name = E_el
[../]
(modules/combined/test/tests/phase_field_fracture/void2d_iso.i)

Input Parameters

  • cOrder parameter for damage

    C++ Type:std::vector

    Options:

    Description:Order parameter for damage

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

    Options:

    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_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

    Options:

    Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

  • F_nameE_elName of material property storing the elastic energy

    Default:E_el

    C++ Type:MaterialPropertyName

    Options:

    Description:Name of material property storing the elastic energy

  • kdamage0Stiffness of damaged matrix

    Default:0

    C++ Type:double

    Options:

    Description:Stiffness of damaged matrix

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

    C++ Type:std::vector

    Options:

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

  • use_current_history_variableFalseUse the current value of the history variable.

    Default:False

    C++ Type:bool

    Options:

    Description:Use the current value of the history variable.

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

    C++ Type:std::vector

    Options:

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

Optional Parameters

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

    C++ Type:std::vector

    Options:

    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

    Options:

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

Outputs Parameters

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

    C++ Type:std::vector

    Options:

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Options:

    Description:Set the enabled status of the MooseObject.

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Options:

    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

    Options:

    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

    Options:NONE ELEMENT SUBDOMAIN

    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

Advanced Parameters

Input Files