Eshelby Tensor

Computes the Eshelby tensor as a function of strain energy density and the first Piola-Kirchhoff stress

Description

This model computes the Eshelby energy-momentum tensor $var element = document.getElementById("moose-equation-6bc35f40-2da1-4322-9a71-3be27a873ef2");katex.render("\\Sigma", element, {displayMode:false,throwOnError:false});$ (Eshelby, 1999), used in fracture integral calculations: $var element = document.getElementById("moose-equation-a6329712-0ccf-45f8-a7e8-24a8a8b22dad");katex.render("\\boldsymbol{\\Sigma} = W\\boldsymbol{I} - \\boldsymbol{H}^T\\boldsymbol{P}", element, {displayMode:true,throwOnError:false});$ where W is the strain energy density in the original configuration, $var element = document.getElementById("moose-equation-16de9824-2314-4e96-890a-eb2b17eafa82");katex.render("\\boldsymbol{I}", element, {displayMode:false,throwOnError:false});$ is the identity matrix, $var element = document.getElementById("moose-equation-8a63749a-c973-4d75-a18c-0d737a3c4b3a");katex.render("\\boldsymbol{H}", element, {displayMode:false,throwOnError:false});$ is the displacement gradient, and $var element = document.getElementById("moose-equation-efd46cbd-53f8-4769-a2ad-c88f9019b6cd");katex.render("\\boldsymbol{P}", element, {displayMode:false,throwOnError:false});$ is the first Piola-Kirchoff stress tensor.

It is necessary to include this material within the input file when computing fracture integrals.

Example Input File Syntax

Input Parameters

displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system

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.
compute_dissipationFalseWhether to compute Eshelby tensor's dissipation (or rate of change). This tensoryields the increase in dissipation per unit crack advanced
Default:False
C++ Type:bool
Controllable:No
Description:Whether to compute Eshelby tensor's dissipation (or rate of change). This tensoryields the increase in dissipation per unit crack advanced
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.
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.
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Controllable:No
Description:Coupled temperature

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

J. D. Eshelby. Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics. In John M. Ball, David Kinderlehrer, Paulo Podio-Guidugli, and Marshall Slemrod, editors, Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids, pages 82–119. Springer Berlin Heidelberg, Berlin, Heidelberg, 1999. doi:10.1007/978-3-642-59938-5\_5.

@incollection{eshelby_energy_1999,
    author = "Eshelby, J. D.",
    editor = "Ball, John M. and Kinderlehrer, David and Podio-Guidugli, Paulo and Slemrod, Marshall",
    address = "Berlin, Heidelberg",
    booktitle = "Fundamental {Contributions} to the {Continuum} {Theory} of {Evolving} {Phase} {Interfaces} in {Solids}",
    language = "en",
    doi = "10.1007/978-3-642-59938-5\\_5",
    pages = "82--119",
    publisher = "Springer Berlin Heidelberg",
    title = "Energy {Relations} and the {Energy}-{Momentum} {Tensor} in {Continuum} {Mechanics}",
    year = "1999"
}