- polar_xThe x component of the polarization
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The x component of the polarization
- polar_yThe y component of the polarization
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The y component of the polarization
RotatedCubicParentFlexoelectricFullEnergy
Calculates the volume integral of the full elastic energy density 1/2 (eps - epsQ - epsF):C:(eps - epsQ - epsF) of a cubic parent phase, electrostrictive and flexoelectric eigenstrains included. The crystal axes are turned by the material property twist about z.
Overview
The elastic energy density of a cubic parent phase with electrostrictive and flexoelectric eigenstrains is
with the electrostrictive and flexoelectric eigenstrains
where is the total strain, the elastic compliance and the flexocoupling tensor. This form is the exact Legendre transform of the Gibbs functional of Gu et al. (2014), including the term.
This postprocessor integrates over the domain for a rotated cubic crystal; it is the energy whose variation is RotatedCubicParentFlexoelectricFullPDerivative.
commentnote:Conventions
mu11, mu12 and mu44 are the tensor components , and of the flexocoupling tensor; the compliances s11, s12, s44 are in Voigt form (). With the sign above, the flexocoupling computed from the published of Gu et al. (2014) is entered directly and gives their tail-to-tail Néel component. The flexoelectric eigenstrain is added to the electrostrictive one (no CompositeEigenstrain weight of ). The deprecated NV/RI flexoelectric objects of earlier development versions carried the shear slot as , i.e. four times too large, and expected the opposite sign.
warningwarning:Literature flexocoupling values
Published flexocoupling tensors come in several index conventions. In particular the displacement-gradient form of Maranganti and Sharma (2009) mixes the 12 and 44 components relative to the strain-gradient form used here, and Voigt shear factors of 1, 2 or 4 appear in the literature. Convert to the tensor components of the strain-gradient form before entering them.
commentnote:Rotated crystal axes
The crystal axes are turned about by the material property twist (radians); the polarization, its gradient and the strain are expressed in the crystal frame, the cubic expressions are evaluated there and the result is turned back. For the displacement equation to see the same crystal, ComputeElasticityTensor must be given euler_angle_3 twist (in degrees).
Example Input File Syntax
[./Fela]
type = RotatedCubicParentFlexoelectricFullEnergy
execute_on = 'timestep_end'
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
block = '0'
[../]Input Parameters
- base_nameMaterial property base name
C++ Type:std::string
Controllable:No
Description:Material property base name
- 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
- energy_scale1the energy scale, useful for transition between eV and J
Default:1
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:the energy scale, useful for transition between eV and J
- polar_zThe z component of the polarization
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The z component of the polarization
Optional Parameters
- allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
- execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
- execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
- force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
- force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
- force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
Execution Scheduling 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
- outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
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
- 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
- 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
Unit:(no unit assumed)
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.
- 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.
Material Property Retrieval Parameters
Input Files
References
- Yijia Gu, Menglei Li, Anna N. Morozovska, Yi Wang, Eugene A. Eliseev, Venkatraman Gopalan, and Long-Qing Chen.
Flexoelectricity and ferroelectric domain wall structures: Phase-field modeling and DFT calculations.
Phys. Rev. B, 89:174111, 2014.
doi:10.1103/PhysRevB.89.174111.[Export]
- R. Maranganti and P. Sharma.
Atomistic determination of flexoelectric properties of crystalline dielectrics.
Phys. Rev. B, 80:054109, 2009.
doi:10.1103/PhysRevB.80.054109.[Export]