This material calculates necessary parameters for the grand potential sintering model. More...

#include <GrandPotentialSinteringMaterial.h>

Inheritance diagram for GrandPotentialSinteringMaterial:

Public Types
typedef DerivativeMaterialPropertyNameInterface::SymbolName	SymbolName

Public Member Functions
	GrandPotentialSinteringMaterial (const InputParameters &parameters)

const GenericMaterialProperty< U, is_ad > &	getDefaultMaterialProperty (const std::string &name)

const GenericMaterialProperty< U, is_ad > &	getDefaultMaterialPropertyByName (const std::string &name)

void	validateDerivativeMaterialPropertyBase (const std::string &base)

const MaterialPropertyName	derivativePropertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	derivativePropertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	derivativePropertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	derivativePropertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, unsigned int v2, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, unsigned int v1, unsigned int v2=libMesh::invalid_uint, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, unsigned int v2, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, unsigned int v1, unsigned int v2=libMesh::invalid_uint, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

void	validateCoupling (const MaterialPropertyName &base, const std::vector< VariableName > &c, bool validate_aux=true)

void	validateCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateCoupling (const MaterialPropertyName &base, const std::vector< VariableName > &c, bool validate_aux=true)

void	validateCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateNonlinearCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateNonlinearCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

const MaterialPropertyName	propertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	propertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	propertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	propertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	propertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	propertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	propertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

const MaterialPropertyName	propertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

Static Public Member Functions
static InputParameters	validParams ()

Protected Member Functions
virtual void	computeQpProperties ()

Protected Attributes
const unsigned int	_neta
	number of solid phase order paramters

std::vector< const VariableValue * >	_eta
	solid phase order parameters

std::vector< VariableName >	_eta_name

const VariableValue &	_w
	chemical potential

const NonlinearVariableName	_w_name

const VariableValue &	_phi
	void phase order parameter

const NonlinearVariableName	_phi_name

const MaterialPropertyName	_cs_eq_name
	equilibrium vacancy concentration

const MaterialProperty< Real > &	_cs_eq

std::vector< const MaterialProperty< Real > * >	_dcs_eq

std::vector< std::vector< const MaterialProperty< Real > * > >	_d2cs_eq

const VariableValue &	_T
	temperature

const MaterialProperty< Real > &	_kv
	void energy coefficient

const MaterialProperty< Real > &	_ks
	solid energy coefficient

MaterialProperty< Real > &	_hv
	void phase switching function

MaterialProperty< Real > &	_dhv

MaterialProperty< Real > &	_d2hv

MaterialProperty< Real > &	_hs
	solid phase switching function

MaterialProperty< Real > &	_dhs

MaterialProperty< Real > &	_d2hs

MaterialProperty< Real > &	_chi
	susceptibility

MaterialProperty< Real > &	_dchidphi

MaterialProperty< Real > &	_dchidw

MaterialProperty< Real > &	_d2chidphi2

MaterialProperty< Real > &	_d2chidw2

MaterialProperty< Real > &	_d2chidphidw

MaterialProperty< Real > &	_rhov
	void phase vacancy density

MaterialProperty< Real > &	_drhovdw

MaterialProperty< Real > &	_rhos
	solid phase vacancy density

MaterialProperty< Real > &	_drhosdw

MaterialProperty< Real > &	_d2rhosdw2

std::vector< MaterialProperty< Real > * >	_drhos

std::vector< MaterialProperty< Real > * >	_d2rhosdwdeta

std::vector< std::vector< MaterialProperty< Real > * > >	_d2rhos

MaterialProperty< Real > &	_omegav
	void phase potential density

MaterialProperty< Real > &	_domegavdw

MaterialProperty< Real > &	_d2omegavdw2

MaterialProperty< Real > &	_omegas
	solid phase potential density

MaterialProperty< Real > &	_domegasdw

MaterialProperty< Real > &	_d2omegasdw2

std::vector< MaterialProperty< Real > * >	_domegasdeta

std::vector< MaterialProperty< Real > * >	_d2omegasdwdeta

std::vector< std::vector< MaterialProperty< Real > * > >	_d2omegasdetadeta

MaterialProperty< Real > &	_mu
	energy barrier coefficient

MaterialProperty< Real > &	_dmu

MaterialProperty< Real > &	_d2mu

MaterialProperty< Real > &	_kappa
	gradient energy coefficient

MaterialProperty< Real > &	_dkappa

MaterialProperty< Real > &	_d2kappa

MaterialProperty< Real > &	_gamma
	interface profile coefficient

MaterialProperty< Real > &	_hv_c_min
	Body Force coefficient for mass conservation in conc and chempot coupling.

MaterialProperty< Real > &	_dhv_c_mindphi

MaterialProperty< Real > &	_d2hv_c_mindphi2

MaterialProperty< Real > &	_hs_c_min

MaterialProperty< Real > &	_dhs_c_mindphi

MaterialProperty< Real > &	_d2hs_c_mindphi2

std::vector< MaterialProperty< Real > * >	_dhs_c_min

std::vector< std::vector< MaterialProperty< Real > * > >	_d2hs_c_min

MaterialProperty< Real > &	_hv_over_kVa
	MatReaction Force coefficient for mass conservation in conc and chempot coupling.

MaterialProperty< Real > &	_dhv_over_kVadphi

MaterialProperty< Real > &	_d2hv_over_kVadphi2

MaterialProperty< Real > &	_hs_over_kVa

MaterialProperty< Real > &	_dhs_over_kVadphi

MaterialProperty< Real > &	_d2hs_over_kVadphi2

const Real	_sigma_s
	surface energy

const Real	_sigma_gb
	grain boundary energy

const Real	_int_width
	interface width

const Real	_switch
	Parameter to determine accuracy of surface/GB phase switching function.

const Real	_Va
	Atomic volume of species.

const MooseEnum	_solid_energy
	Type of energy function to use for the solid phase.

const Real	_mu_s
	mu value on surfaces

const Real	_mu_gb
	mu value on grain boundaries

const Real	_kappa_s
	kappa value on surfaces

const Real	_kappa_gb
	kappa value on grain boundaries

const Real	_kB
	Boltzmann constant.

const bool	_mass_conservation
	strict mass conservation flag

Private Member Functions
bool	haveMaterialProperty (const std::string &prop_name)

std::vector< VariableName >	buildVariableVector (const VariableName &c1, const VariableName &c2, const VariableName &c3)

void	validateCouplingHelper (const MaterialPropertyName &base, const std::vector< VariableName > &c, const System &system, std::vector< VariableName > &missing)

bool	isNotObjectVariable (const VariableName &name)

Private Attributes
FEProblemBase &	_dmi_fe_problem

Detailed Description

This material calculates necessary parameters for the grand potential sintering model.

Especially those related to switching functions and thermodynamics.

Definition at line 19 of file GrandPotentialSinteringMaterial.h.

Constructor & Destructor Documentation

◆ GrandPotentialSinteringMaterial()

GrandPotentialSinteringMaterial::GrandPotentialSinteringMaterial ( const InputParameters & parameters )

Definition at line 55 of file GrandPotentialSinteringMaterial.C.

  : DerivativeMaterialInterface<Material>(parameters),
    _neta(coupledComponents("etas")),
    _eta(_neta),
    _eta_name(_neta),
    _w(coupledValue("chemical_potential")),
    _w_name(coupledName("chemical_potential", 0)),
    _phi(coupledValue("void_op")),
    _phi_name(coupledName("void_op", 0)),
    _cs_eq_name(getParam<MaterialPropertyName>("equilibrium_vacancy_concentration")),
    _cs_eq(getMaterialProperty<Real>(_cs_eq_name)),
    _dcs_eq(_neta),
    _d2cs_eq(_neta),
    _T(coupledValue("Temperature")),
    _kv(getMaterialProperty<Real>("void_energy_coefficient")),
    _ks(getMaterialProperty<Real>("solid_energy_coefficient")),
    _hv(declareProperty<Real>("hv")),
    _dhv(declarePropertyDerivative<Real>("hv", _phi_name)),
    _d2hv(declarePropertyDerivative<Real>("hv", _phi_name, _phi_name)),
    _hs(declareProperty<Real>("hs")),
    _dhs(declarePropertyDerivative<Real>("hs", _phi_name)),
    _d2hs(declarePropertyDerivative<Real>("hs", _phi_name, _phi_name)),
    _chi(declareProperty<Real>("chi")),
    _dchidphi(declarePropertyDerivative<Real>("chi", _phi_name)),
    _dchidw(declarePropertyDerivative<Real>("chi", _w_name)),
    _d2chidphi2(declarePropertyDerivative<Real>("chi", _phi_name, _phi_name)),
    _d2chidw2(declarePropertyDerivative<Real>("chi", _w_name, _w_name)),
    _d2chidphidw(declarePropertyDerivative<Real>("chi", _phi_name, _w_name)),
    _rhov(declareProperty<Real>("rhov")),
    _drhovdw(declarePropertyDerivative<Real>("rhov", _w_name)),
    _rhos(declareProperty<Real>("rhos")),
    _drhosdw(declarePropertyDerivative<Real>("rhos", _w_name)),
    _d2rhosdw2(declarePropertyDerivative<Real>("rhos", _w_name, _w_name)),
    _drhos(_neta),
    _d2rhosdwdeta(_neta),
    _d2rhos(_neta),
    _omegav(declareProperty<Real>("omegav")),
    _domegavdw(declarePropertyDerivative<Real>("omegav", _w_name)),
    _d2omegavdw2(declarePropertyDerivative<Real>("omegav", _w_name, _w_name)),
    _omegas(declareProperty<Real>("omegas")),
    _domegasdw(declarePropertyDerivative<Real>("omegas", _w_name)),
    _d2omegasdw2(declarePropertyDerivative<Real>("omegas", _w_name, _w_name)),
    _domegasdeta(_neta),
    _d2omegasdwdeta(_neta),
    _d2omegasdetadeta(_neta),
    _mu(declareProperty<Real>("mu")),
    _dmu(declarePropertyDerivative<Real>("mu", _phi_name)),
    _d2mu(declarePropertyDerivative<Real>("mu", _phi_name, _phi_name)),
    _kappa(declareProperty<Real>("kappa")),
    _dkappa(declarePropertyDerivative<Real>("kappa", _phi_name)),
    _d2kappa(declarePropertyDerivative<Real>("kappa", _phi_name, _phi_name)),
    _gamma(declareProperty<Real>("gamma")),
    _hv_c_min(declareProperty<Real>("hv_c_min")),
    _dhv_c_mindphi(declarePropertyDerivative<Real>("hv_c_min", _phi_name)),
    _d2hv_c_mindphi2(declarePropertyDerivative<Real>("hv_c_min", _phi_name, _phi_name)),
    _hs_c_min(declareProperty<Real>("hs_c_min")),
    _dhs_c_mindphi(declarePropertyDerivative<Real>("hs_c_min", _phi_name)),
    _d2hs_c_mindphi2(declarePropertyDerivative<Real>("hs_c_min", _phi_name, _phi_name)),
    _dhs_c_min(_neta),
    _d2hs_c_min(_neta),
    _hv_over_kVa(declareProperty<Real>("hv_over_kVa")),
    _dhv_over_kVadphi(declarePropertyDerivative<Real>("hv_over_kVa", _phi_name)),
    _d2hv_over_kVadphi2(declarePropertyDerivative<Real>("hv_over_kVa", _phi_name, _phi_name)),
    _hs_over_kVa(declareProperty<Real>("hs_over_kVa")),
    _dhs_over_kVadphi(declarePropertyDerivative<Real>("hs_over_kVa", _phi_name)),
    _d2hs_over_kVadphi2(declarePropertyDerivative<Real>("hs_over_kVa", _phi_name, _phi_name)),
 
    _sigma_s(getParam<Real>("surface_energy")),
    _sigma_gb(getParam<Real>("grainboundary_energy")),
    _int_width(getParam<Real>("int_width")),
    _switch(getParam<Real>("surface_switch_value")),
    _Va(getParam<Real>("atomic_volume")),
    _solid_energy(getParam<MooseEnum>("solid_energy_model")),
    _mu_s(6.0 * _sigma_s / _int_width),
    _mu_gb(6.0 * _sigma_gb / _int_width),
    _kappa_s(0.75 * _sigma_s * _int_width),
    _kappa_gb(0.75 * _sigma_gb * _int_width),
    _kB(8.617343e-5), // eV/K
    _mass_conservation(getParam<bool>("mass_conservation"))
{
  if ((_switch > 1.0) || (_switch < 0.0))
    mooseError("GrandPotentialSinteringMaterial: surface_switch_value should be between 0 and 1");
 
  if (_mass_conservation && _solid_energy > 0)
    mooseError("GrandPotentialSinteringMaterial: strict mass conservation is currently only "
               "applicable to parabolic free energy");
 
  for (unsigned int i = 0; i < _neta; ++i)
  {
    _eta[i] = &coupledValue("etas", i);
    _eta_name[i] = coupledName("etas", i);
    _dcs_eq[i] = &getMaterialPropertyDerivativeByName<Real>(_cs_eq_name, _eta_name[i]);
    _d2cs_eq[i].resize(_neta);
    _drhos[i] = &declarePropertyDerivative<Real>("rhos", _eta_name[i]);
    _d2rhos[i].resize(_neta);
    _d2rhosdwdeta[i] = &declarePropertyDerivative<Real>("rhos", _w_name, _eta_name[i]);
    _domegasdeta[i] = &declarePropertyDerivative<Real>("omegas", _eta_name[i]);
    _d2omegasdwdeta[i] = &declarePropertyDerivative<Real>("omegas", _w_name, _eta_name[i]);
    _d2omegasdetadeta[i].resize(_neta);
    _dhs_c_min[i] = &declarePropertyDerivative<Real>("hs_c_min", _eta_name[i]);
    _d2hs_c_min[i].resize(_neta);
 
    for (unsigned int j = 0; j <= i; ++j)
    {
      _d2cs_eq[j][i] =
          &getMaterialPropertyDerivativeByName<Real>(_cs_eq_name, _eta_name[j], _eta_name[i]);
      _d2rhos[j][i] = &declarePropertyDerivative<Real>("rhos", _eta_name[j], _eta_name[i]);
      _d2omegasdetadeta[j][i] =
          &declarePropertyDerivative<Real>("omegas", _eta_name[j], _eta_name[i]);
      _d2hs_c_min[j][i] = &declarePropertyDerivative<Real>("hs_c_min", _eta_name[j], _eta_name[i]);
    }
  }
}

Member Function Documentation

◆ computeQpProperties()

void GrandPotentialSinteringMaterial::computeQpProperties ( )

protectedvirtual

Definition at line 170 of file GrandPotentialSinteringMaterial.C.

{
  // Calculate phase switching functions
  _hv[_qp] = 0.0;
  _dhv[_qp] = 0.0;
  _d2hv[_qp] = 0.0;
 
  if (_phi[_qp] >= 1.0)
    _hv[_qp] = 1.0;
  else if (_phi[_qp] > 0.0)
  {
    _hv[_qp] = _phi[_qp] * _phi[_qp] * _phi[_qp] * (10.0 + _phi[_qp] * (-15.0 + _phi[_qp] * 6.0));
    _dhv[_qp] = 30.0 * _phi[_qp] * _phi[_qp] * (_phi[_qp] - 1.0) * (_phi[_qp] - 1.0);
    _d2hv[_qp] = 60.0 * _phi[_qp] * (2.0 * _phi[_qp] - 1.0) * (_phi[_qp] - 1.0);
  }
 
  _hs[_qp] = 1.0 - _hv[_qp];
  _dhs[_qp] = -_dhv[_qp];
  _d2hs[_qp] = -_d2hv[_qp];
 
  // Calculate interface switching function
  Real phi = _phi[_qp] / _switch;
  Real f = 0.0;
  Real df = 0.0;
  Real d2f = 0.0;
  if (phi >= 1.0)
    f = 1.0;
  else if (phi > 0.0)
  {
    f = phi * phi * phi * (10.0 + phi * (-15.0 + phi * 6.0));
    df = 30.0 / _switch * phi * phi * (phi - 1.0) * (phi - 1.0);
    d2f = 60.0 * phi / (_switch * _switch) * (2.0 * phi - 1.0) * (phi - 1.0);
  }
 
  // Equilibrium vacancy concentration
  Real cv_eq = 1.0;
 
  // Calculate the void phase density and potentials
  _rhov[_qp] = _w[_qp] / (_Va * _Va * _kv[_qp]) + cv_eq / _Va;
  _drhovdw[_qp] = 1.0 / (_Va * _Va * _kv[_qp]);
 
  _omegav[_qp] = -0.5 * _w[_qp] * _w[_qp] / (_Va * _Va * _kv[_qp]) - _w[_qp] * cv_eq / _Va;
  _domegavdw[_qp] = -_rhov[_qp];
  _d2omegavdw2[_qp] = -_drhovdw[_qp];
 
  // Calculate solid phase density and potential
  Real d3rhosdw3 = 0;
  switch (_solid_energy)
  {
    case 0: // PARABOLIC
    {
      _rhos[_qp] = _w[_qp] / (_Va * _Va * _ks[_qp]) + _cs_eq[_qp] / _Va;
      _drhosdw[_qp] = 1.0 / (_Va * _Va * _ks[_qp]);
      _d2rhosdw2[_qp] = 0.0;
      d3rhosdw3 = 0.0;
 
      _omegas[_qp] =
          -0.5 * _w[_qp] * _w[_qp] / (_Va * _Va * _ks[_qp]) - _w[_qp] * _cs_eq[_qp] / _Va;
      _domegasdw[_qp] = -_rhos[_qp];
      _d2omegasdw2[_qp] = -_drhosdw[_qp];
 
      // bodyforce and matreact coefficients for strict mass conservation case
      _hv_c_min[_qp] = _hv[_qp] * 1.0;
      _dhv_c_mindphi[_qp] = _dhv[_qp] * 1.0;
      _d2hv_c_mindphi2[_qp] = _d2hv[_qp] * 1.0;
      _hs_c_min[_qp] = _hs[_qp] * _cs_eq[_qp];
      _dhs_c_mindphi[_qp] = _dhs[_qp] * _cs_eq[_qp];
      _d2hs_c_mindphi2[_qp] = _d2hs[_qp] * _cs_eq[_qp];
      _hv_over_kVa[_qp] = _hv[_qp] / (_Va * _kv[_qp]);
      _dhv_over_kVadphi[_qp] = _dhv[_qp] / (_Va * _kv[_qp]);
      _d2hv_over_kVadphi2[_qp] = _d2hv[_qp] / (_Va * _kv[_qp]);
      _hs_over_kVa[_qp] = _hs[_qp] / (_Va * _ks[_qp]);
      _dhs_over_kVadphi[_qp] = _dhs[_qp] / (_Va * _ks[_qp]);
      _d2hs_over_kVadphi2[_qp] = _d2hs[_qp] / (_Va * _ks[_qp]);
 
      for (unsigned int i = 0; i < _neta; ++i)
      {
        (*_drhos[i])[_qp] = (*_dcs_eq[i])[_qp] / _Va;
        (*_d2rhosdwdeta[i])[_qp] = 0.0;
        (*_domegasdeta[i])[_qp] = -_w[_qp] * (*_dcs_eq[i])[_qp] / _Va;
        (*_d2omegasdwdeta[i])[_qp] = -(*_dcs_eq[i])[_qp] / _Va;
        (*_dhs_c_min[i])[_qp] = _hs[_qp] * (*_dcs_eq[i])[_qp];
        for (unsigned int j = i; j < _neta; ++j)
        {
          (*_d2rhos[i][j])[_qp] = (*_d2cs_eq[i][j])[_qp] / _Va;
          (*_d2omegasdetadeta[i][j])[_qp] = -_w[_qp] * (*_d2cs_eq[i][j])[_qp] / _Va;
          (*_d2hs_c_min[i][j])[_qp] = _hs[_qp] * (*_d2cs_eq[i][j])[_qp];
        }
      }
      break;
    } // case 0; // PARABOLIC
    case 1: // DILUTE
    {
      Real rho_exp = std::exp(_w[_qp] / _kB / _T[_qp]);
      _rhos[_qp] = _cs_eq[_qp] / _Va * rho_exp;
      _drhosdw[_qp] = _rhos[_qp] / _kB / _T[_qp];
      _d2rhosdw2[_qp] = _drhosdw[_qp] / _kB / _T[_qp];
      d3rhosdw3 = _d2rhosdw2[_qp] / _kB / _T[_qp];
 
      _omegas[_qp] = _kB * _T[_qp] * (_cs_eq[_qp] / _Va - _rhos[_qp]);
      _domegasdw[_qp] = -_rhos[_qp];
      _d2omegasdw2[_qp] = -_drhosdw[_qp];
      for (unsigned int i = 0; i < _neta; ++i)
      {
        (*_drhos[i])[_qp] = (*_dcs_eq[i])[_qp] * rho_exp / _Va;
        (*_d2rhosdwdeta[i])[_qp] = 0.0;
        (*_domegasdeta[i])[_qp] = _kB * _T[_qp] * (*_dcs_eq[i])[_qp] / _Va * (1.0 - rho_exp);
        (*_d2omegasdwdeta[i])[_qp] = -1.0 / _Va * (*_dcs_eq[i])[_qp] * rho_exp;
        for (unsigned int j = i; j < _neta; ++j)
        {
          (*_d2rhos[i][j])[_qp] = (*_d2cs_eq[i][j])[_qp] * rho_exp / _Va;
          (*_d2omegasdetadeta[i][j])[_qp] =
              _kB * _T[_qp] * (*_d2cs_eq[i][j])[_qp] / _Va * (1.0 - rho_exp);
        }
      }
      break;
    } // case 1: // DILUTE
    case 2: // IDEAL
    {
      Real Ef = -_kB * _T[_qp] * std::log(_cs_eq[_qp] / (1.0 - _cs_eq[_qp]));
      std::vector<Real> dEf;
      std::vector<std::vector<Real>> d2Ef;
      dEf.resize(_neta);
      d2Ef.resize(_neta);
 
      Real x = std::exp((_w[_qp] - Ef) / (_kB * _T[_qp]));
      Real x0 = std::exp(-Ef / (_kB * _T[_qp]));
      _rhos[_qp] = x / ((1.0 + x) * _Va);
      Real rhos0 = x0 / ((1.0 + x0) * _Va);
      _drhosdw[_qp] = x / (Utility::pow<2>(1.0 + x) * _Va * _kB * _T[_qp]);
      _d2rhosdw2[_qp] =
          x * (1.0 - x) / (_Va * Utility::pow<2>(_kB * _T[_qp]) * Utility::pow<3>(1.0 + x));
      d3rhosdw3 = x * (1 - 4.0 * x + x * x) /
                  (_Va * Utility::pow<3>(_kB * _T[_qp]) * Utility::pow<4>(1.0 + x));
 
      _omegas[_qp] = _kB * _T[_qp] / _Va * (std::log(1.0 + x0) - std::log(1.0 + x));
      _domegasdw[_qp] = -_rhos[_qp];
      _d2omegasdw2[_qp] = -_drhosdw[_qp];
      for (unsigned int i = 0; i < _neta; ++i)
      {
        dEf[i] =
            -_kB * _T[_qp] * (*_dcs_eq[i])[_qp] * (1.0 / _cs_eq[_qp] + 1.0 / (1.0 - _cs_eq[_qp]));
        d2Ef[i].resize(_neta);
 
        (*_drhos[i])[_qp] = -dEf[i] * _drhosdw[_qp];
        (*_d2rhosdwdeta[i])[_qp] = -dEf[i] * _d2rhosdw2[_qp];
 
        (*_domegasdeta[i])[_qp] = dEf[i] * (_rhos[_qp] - rhos0);
        (*_d2omegasdwdeta[i])[_qp] = dEf[i] * _drhosdw[_qp];
 
        for (unsigned int j = i; j < _neta; ++j)
        {
          d2Ef[i][j] = -_kB * _T[_qp] *
                       ((*_d2cs_eq[i][j])[_qp] * (1.0 / _cs_eq[_qp] + 1.0 / (1.0 - _cs_eq[_qp])) +
                        (*_dcs_eq[i])[_qp] * (*_dcs_eq[j])[_qp] *
                            (1.0 / ((1.0 - _cs_eq[_qp]) * (1.0 - _cs_eq[_qp])) -
                             1.0 / (_cs_eq[_qp] * _cs_eq[_qp])));
 
          (*_d2rhos[i][j])[_qp] = -d2Ef[i][j] * _drhosdw[_qp] + dEf[i] * dEf[j] * _d2rhosdw2[_qp];
          (*_d2omegasdetadeta[i][j])[_qp] =
              d2Ef[i][j] * (_rhos[_qp] - rhos0) +
              dEf[i] * dEf[j] / (_Va * _kB * _T[_qp]) *
                  (x / Utility::pow<2>(1.0 + x) - x0 / Utility::pow<2>(1.0 + x0));
        }
      }
      break;
    } // case 2: // IDEAL
  } // switch (_solid_energy)
 
  // Calculate the susceptibility
  _chi[_qp] = _hs[_qp] * _drhosdw[_qp] + _hv[_qp] * _drhovdw[_qp];
  _dchidphi[_qp] = _dhs[_qp] * _drhosdw[_qp] + _dhv[_qp] * _drhovdw[_qp];
  _dchidw[_qp] = _hs[_qp] * _d2rhosdw2[_qp];
  _d2chidphi2[_qp] = _d2hs[_qp] * _drhosdw[_qp] + _d2hv[_qp] * _drhovdw[_qp];
  _d2chidw2[_qp] = _hs[_qp] * d3rhosdw3;
  _d2chidphidw[_qp] = _dhs[_qp] * _d2rhosdw2[_qp];
 
  // thermodynamic parameters
  _mu[_qp] = _mu_gb + (_mu_s - _mu_gb) * f;
  _kappa[_qp] = _kappa_gb + (_kappa_s - _kappa_gb) * f;
  _dmu[_qp] = (_mu_s - _mu_gb) * df;
  _dkappa[_qp] = (_kappa_s - _kappa_gb) * df;
  _d2mu[_qp] = (_mu_s - _mu_gb) * d2f;
  _d2kappa[_qp] = (_kappa_s - _kappa_gb) * d2f;
  _gamma[_qp] = 1.5;
} // void GrandPotentialSinteringMaterial::computeQpProperties()

◆ validParams()

InputParameters GrandPotentialSinteringMaterial::validParams ( )

static

Definition at line 17 of file GrandPotentialSinteringMaterial.C.

{
  InputParameters params = Material::validParams();
  params.addClassDescription(
      "Includes switching and thermodynamic properties for the grand potential sintering model");
  params.addRequiredCoupledVarWithAutoBuild(
      "etas", "var_name_base", "op_num", "Array of order parameters that describe solid phase");
  params.addRequiredCoupledVar("chemical_potential", "The name of the chemical potential variable");
  params.addRequiredCoupledVar("void_op", "The name of the void phase order parameter");
  params.addRequiredCoupledVar("Temperature", "Name of the temperature variable with units of K");
  params.addParam<MaterialPropertyName>(
      "solid_energy_coefficient",
      1.0,
      "Parabolic solid energy coefficient (energy/volume). Only used for parabolic energy.");
  params.addRequiredParam<MaterialPropertyName>(
      "void_energy_coefficient", "Parabolic void energy coefficient (energy/volume)");
  params.addParam<Real>("surface_energy", 19.7, "Surface energy in units of problem (energy/area)");
  params.addParam<Real>(
      "grainboundary_energy", 9.86, "Grain boundary energy in units of problem (energy/area)");
  params.addParam<Real>("int_width", 1, "Interface width in units of problem (length)");
  params.addParam<Real>("surface_switch_value",
                        0.3,
                        "Value between 0 and 1 that determines when the interface begins to switch "
                        "from surface to GB. Small values give less error while large values "
                        "converge better.");
  params.addRequiredParam<MaterialPropertyName>(
      "equilibrium_vacancy_concentration",
      "Name of material that determines the equilibrium vacancy concentration in the solid phase");
  params.addParam<Real>("atomic_volume", 0.04092, "Atomic volume of material");
  MooseEnum solid_energy_model("PARABOLIC DILUTE IDEAL", "PARABOLIC");
  params.addParam<MooseEnum>("solid_energy_model",
                             solid_energy_model,
                             "Type of energy function to use for the solid phase.");
  params.addParam<bool>(
      "mass_conservation", false, "imposing strict mass conservation formulation");
  return params;
}

Member Data Documentation

◆ _chi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_chi

protected

susceptibility

Definition at line 69 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _cs_eq

const MaterialProperty<Real>& GrandPotentialSinteringMaterial::_cs_eq

protected

Definition at line 46 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _cs_eq_name

const MaterialPropertyName GrandPotentialSinteringMaterial::_cs_eq_name

protected

equilibrium vacancy concentration

Definition at line 45 of file GrandPotentialSinteringMaterial.h.

Referenced by GrandPotentialSinteringMaterial().

◆ _d2chidphi2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2chidphi2

protected

Definition at line 72 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2chidphidw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2chidphidw

protected

Definition at line 74 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2chidw2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2chidw2

protected

Definition at line 73 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2cs_eq

std::vector<std::vector<const MaterialProperty<Real> *> > GrandPotentialSinteringMaterial::_d2cs_eq

protected

Definition at line 48 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _d2hs

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hs

protected

Definition at line 66 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hs_c_min

std::vector<std::vector<MaterialProperty<Real> *> > GrandPotentialSinteringMaterial::_d2hs_c_min

protected

Definition at line 122 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _d2hs_c_mindphi2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hs_c_mindphi2

protected

Definition at line 120 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hs_over_kVadphi2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hs_over_kVadphi2

protected

Definition at line 130 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hv

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hv

protected

Definition at line 61 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hv_c_mindphi2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hv_c_mindphi2

protected

Definition at line 117 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hv_over_kVadphi2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2hv_over_kVadphi2

protected

Definition at line 127 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2kappa

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2kappa

protected

Definition at line 109 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2mu

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2mu

protected

Definition at line 104 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2omegasdetadeta

std::vector<std::vector<MaterialProperty<Real> *> > GrandPotentialSinteringMaterial::_d2omegasdetadeta

protected

Definition at line 99 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _d2omegasdw2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2omegasdw2

protected

Definition at line 96 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2omegasdwdeta

std::vector<MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_d2omegasdwdeta

protected

Definition at line 98 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _d2omegavdw2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2omegavdw2

protected

Definition at line 91 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2rhos

std::vector<std::vector<MaterialProperty<Real> *> > GrandPotentialSinteringMaterial::_d2rhos

protected

Definition at line 86 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _d2rhosdw2

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_d2rhosdw2

protected

Definition at line 83 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2rhosdwdeta

std::vector<MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_d2rhosdwdeta

protected

Definition at line 85 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _dchidphi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dchidphi

protected

Definition at line 70 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dchidw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dchidw

protected

Definition at line 71 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dcs_eq

std::vector<const MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_dcs_eq

protected

Definition at line 47 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _dhs

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhs

protected

Definition at line 65 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhs_c_min

std::vector<MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_dhs_c_min

protected

Definition at line 121 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _dhs_c_mindphi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhs_c_mindphi

protected

Definition at line 119 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhs_over_kVadphi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhs_over_kVadphi

protected

Definition at line 129 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhv

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhv

protected

Definition at line 60 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhv_c_mindphi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhv_c_mindphi

protected

Definition at line 116 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhv_over_kVadphi

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dhv_over_kVadphi

protected

Definition at line 126 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dkappa

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dkappa

protected

Definition at line 108 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dmu

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_dmu

protected

Definition at line 103 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _domegasdeta

std::vector<MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_domegasdeta

protected

Definition at line 97 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _domegasdw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_domegasdw

protected

Definition at line 95 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _domegavdw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_domegavdw

protected

Definition at line 90 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _drhos

std::vector<MaterialProperty<Real> *> GrandPotentialSinteringMaterial::_drhos

protected

Definition at line 84 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _drhosdw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_drhosdw

protected

Definition at line 82 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _drhovdw

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_drhovdw

protected

Definition at line 78 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _eta

std::vector<const VariableValue *> GrandPotentialSinteringMaterial::_eta

protected

solid phase order parameters

Definition at line 33 of file GrandPotentialSinteringMaterial.h.

Referenced by GrandPotentialSinteringMaterial().

◆ _eta_name

std::vector<VariableName> GrandPotentialSinteringMaterial::_eta_name

protected

Definition at line 34 of file GrandPotentialSinteringMaterial.h.

Referenced by GrandPotentialSinteringMaterial().

◆ _gamma

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_gamma

protected

interface profile coefficient

Definition at line 112 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hs

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hs

protected

solid phase switching function

Definition at line 64 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hs_c_min

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hs_c_min

protected

Definition at line 118 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hs_over_kVa

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hs_over_kVa

protected

Definition at line 128 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hv

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hv

protected

void phase switching function

Definition at line 59 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hv_c_min

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hv_c_min

protected

Body Force coefficient for mass conservation in conc and chempot coupling.

Definition at line 115 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hv_over_kVa

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_hv_over_kVa

protected

MatReaction Force coefficient for mass conservation in conc and chempot coupling.

Definition at line 125 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _int_width

const Real GrandPotentialSinteringMaterial::_int_width

protected

interface width

Definition at line 139 of file GrandPotentialSinteringMaterial.h.

◆ _kappa

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_kappa

protected

gradient energy coefficient

Definition at line 107 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kappa_gb

const Real GrandPotentialSinteringMaterial::_kappa_gb

protected

kappa value on grain boundaries

Definition at line 160 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kappa_s

const Real GrandPotentialSinteringMaterial::_kappa_s

protected

kappa value on surfaces

Definition at line 157 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kB

const Real GrandPotentialSinteringMaterial::_kB

protected

Boltzmann constant.

Definition at line 163 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _ks

const MaterialProperty<Real>& GrandPotentialSinteringMaterial::_ks

protected

solid energy coefficient

Definition at line 56 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kv

const MaterialProperty<Real>& GrandPotentialSinteringMaterial::_kv

protected

void energy coefficient

Definition at line 54 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _mass_conservation

const bool GrandPotentialSinteringMaterial::_mass_conservation

protected

strict mass conservation flag

Definition at line 166 of file GrandPotentialSinteringMaterial.h.

Referenced by GrandPotentialSinteringMaterial().

◆ _mu

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_mu

protected

energy barrier coefficient

Definition at line 102 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _mu_gb

const Real GrandPotentialSinteringMaterial::_mu_gb

protected

mu value on grain boundaries

Definition at line 154 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _mu_s

const Real GrandPotentialSinteringMaterial::_mu_s

protected

mu value on surfaces

Definition at line 151 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _neta

const unsigned int GrandPotentialSinteringMaterial::_neta

protected

number of solid phase order paramters

Definition at line 30 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _omegas

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_omegas

protected

solid phase potential density

Definition at line 94 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _omegav

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_omegav

protected

void phase potential density

Definition at line 89 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _phi

const VariableValue& GrandPotentialSinteringMaterial::_phi

protected

void phase order parameter

Definition at line 41 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _phi_name

const NonlinearVariableName GrandPotentialSinteringMaterial::_phi_name

protected

Definition at line 42 of file GrandPotentialSinteringMaterial.h.

◆ _rhos

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_rhos

protected

solid phase vacancy density

Definition at line 81 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _rhov

MaterialProperty<Real>& GrandPotentialSinteringMaterial::_rhov

protected

void phase vacancy density

Definition at line 77 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _sigma_gb

const Real GrandPotentialSinteringMaterial::_sigma_gb

protected

grain boundary energy

Definition at line 136 of file GrandPotentialSinteringMaterial.h.

◆ _sigma_s

const Real GrandPotentialSinteringMaterial::_sigma_s

protected

surface energy

Definition at line 133 of file GrandPotentialSinteringMaterial.h.

◆ _solid_energy

const MooseEnum GrandPotentialSinteringMaterial::_solid_energy

protected

Type of energy function to use for the solid phase.

Definition at line 148 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _switch

const Real GrandPotentialSinteringMaterial::_switch

protected

Parameter to determine accuracy of surface/GB phase switching function.

Definition at line 142 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties(), and GrandPotentialSinteringMaterial().

◆ _T

const VariableValue& GrandPotentialSinteringMaterial::_T

protected

temperature

Definition at line 51 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _Va

const Real GrandPotentialSinteringMaterial::_Va

protected

Atomic volume of species.

Definition at line 145 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _w

const VariableValue& GrandPotentialSinteringMaterial::_w

protected

chemical potential

Definition at line 37 of file GrandPotentialSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _w_name

const NonlinearVariableName GrandPotentialSinteringMaterial::_w_name

protected

Definition at line 38 of file GrandPotentialSinteringMaterial.h.

Referenced by GrandPotentialSinteringMaterial().

The documentation for this class was generated from the following files:

phase_field/include/materials/GrandPotentialSinteringMaterial.h
phase_field/src/materials/GrandPotentialSinteringMaterial.C

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ GrandPotentialSinteringMaterial()

Member Function Documentation

◆ computeQpProperties()

◆ validParams()

Member Data Documentation

◆ _chi

◆ _cs_eq

◆ _cs_eq_name

◆ _d2chidphi2

◆ _d2chidphidw

◆ _d2chidw2

◆ _d2cs_eq

◆ _d2hs

◆ _d2hs_c_min

◆ _d2hs_c_mindphi2

◆ _d2hs_over_kVadphi2

◆ _d2hv

◆ _d2hv_c_mindphi2

◆ _d2hv_over_kVadphi2

◆ _d2kappa

◆ _d2mu

◆ _d2omegasdetadeta

◆ _d2omegasdw2

◆ _d2omegasdwdeta

◆ _d2omegavdw2

◆ _d2rhos

◆ _d2rhosdw2

◆ _d2rhosdwdeta

◆ _dchidphi

◆ _dchidw

◆ _dcs_eq

◆ _dhs

◆ _dhs_c_min

◆ _dhs_c_mindphi

◆ _dhs_over_kVadphi

◆ _dhv

◆ _dhv_c_mindphi

◆ _dhv_over_kVadphi

◆ _dkappa

◆ _dmu

◆ _domegasdeta

◆ _domegasdw

◆ _domegavdw

◆ _drhos

◆ _drhosdw

◆ _drhovdw

◆ _eta

◆ _eta_name

◆ _gamma

◆ _hs

◆ _hs_c_min

◆ _hs_over_kVa

◆ _hv

◆ _hv_c_min

◆ _hv_over_kVa

◆ _int_width

◆ _kappa

◆ _kappa_gb

◆ _kappa_s

◆ _kB

◆ _ks

◆ _kv

◆ _mass_conservation

◆ _mu

◆ _mu_gb

◆ _mu_s

◆ _neta

◆ _omegas

◆ _omegav

◆ _phi

◆ _phi_name