LDLNucleationMicroForce

This class computes the external driving force for nucleation given a Drucker-Prager strength envelope developed by Larsen et al. (2024)

See A variational formulation of Griffith phase-field fracture with material strength by Larsen et al. (2024)

This is a variational recast of the phase-field fracture formulation put forth by Kumar, Francfort and Lopez-Pamies (2018), where is explicitly evaluated.

Overview

LDL (Larsen, Dolbow, Lopez) Model 2024

The fracture functional reads

The governing equation for fracture is

Note that the following derivation follows settings of AT-1, i.e., and . In this model, the strict irreversibility condition for is adopted.

The "undamaged" nucleation driving force is defined as

In this recast, is evaluated explicitly as

where

with

The material properties used are the bulk modulus and Young's modulus and the shear modulus .

The strength surface is presented with uniaxial tensile and hydrostatic strength , where .

KLR (Kumar, Lopez, Ravi-Chandar) Model 2022

Please see KLRNucleationMicroForce

KLBF (Kumar, Lopez, Bourdin, Francfort) Model 2020

Please see KLBFNucleationMicroForce

Example Input File Syntax


[Materials]
  [micro_force]
    type = LDLNucleationMicroForce
    regularization_length = l
    normalization_constant = c0
    tensile_strength = sigma_ts
    hydrostatic_strength = sigma_hs
    external_driving_force_name = ce
    h_correction = true
  []
[]

Input Parameters

  • hydrostatic_strengthThe hydrostatic strength of the material beyond which the material fails.

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:The hydrostatic strength of the material beyond which the material fails.

  • phase_fieldName of the phase-field (damage) variable

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:Name of the phase-field (damage) variable

  • tensile_strengthThe tensile strength of the material beyond which the material fails.

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:The tensile strength of the material beyond which the material fails.

Required Parameters

  • 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

  • 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

  • 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.

  • degradation_functiongThe degradation function

    Default:g

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:The degradation function

  • deltadeltaName of the unitless coefficient delta

    Default:delta

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:Name of the unitless coefficient delta

  • external_driving_force_nameex_drivingName of the material that holds the external_driving_force

    Default:ex_driving

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:Name of the material that holds the external_driving_force

  • fracture_toughnessGcenergy release rate or fracture toughness

    Default:Gc

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:energy release rate or fracture toughness

  • h_correctionFalseWhether to use h correction formula for delta

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether to use h correction formula for delta

  • lambdalambdaLame's first parameter lambda

    Default:lambda

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:Lame's first parameter lambda

  • normalization_constantc0The normalization constant $c_0$

    Default:c0

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:The normalization constant $c_0$

  • 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.

  • regularization_lengthlthe phase field regularization length

    Default:l

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:the phase field regularization length

  • shear_modulusGshear modulus mu or G

    Default:G

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:shear modulus mu or G

  • stress_balance_namestress_balanceName of the stress balance function $F(\sigma)$

    Default:stress_balance

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:Name of the stress balance function $F(\sigma)$

  • stress_namestressName of the stress tensor

    Default:stress

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:Name of the stress tensor

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

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

Input Files

References

  1. C. J. Larsen, J. E. Dolbow, and O. Lopez-Pamies. A variational formulation of griffith phase-field fracture with material strength. Arxiv, 2024. URL: https://arxiv.org/abs/2401.13938.[BibTeX]