Real
DerivativeTwoPhaseMaterial::computeD3F(unsigned int i_var, unsigned int j_var, unsigned int k_var)
{
if (i_var == _eta_var && j_var == _eta_var && k_var == _eta_var)
return _d3h[_qp] * (_prop_Fb[_qp] - _prop_Fa[_qp]) + _W * _d3g[_qp];
unsigned int i = argIndex(i_var);
unsigned int j = argIndex(j_var);
unsigned int k = argIndex(k_var);
if (j_var == _eta_var && k_var == _eta_var)
return _d2h[_qp] * ((*_prop_dFb[i])[_qp] - (*_prop_dFa[i])[_qp]);
if (i_var == _eta_var && k_var == _eta_var)
return _d2h[_qp] * ((*_prop_dFb[j])[_qp] - (*_prop_dFa[j])[_qp]);
if (i_var == _eta_var && j_var == _eta_var)
return _d2h[_qp] * ((*_prop_dFb[k])[_qp] - (*_prop_dFa[k])[_qp]);
if (i_var == _eta_var)
return _dh[_qp] * (*_prop_d2Fb[j][k])[_qp] + (1.0 - _dh[_qp]) * (*_prop_d2Fa[j][k])[_qp];
if (j_var == _eta_var)
return _dh[_qp] * (*_prop_d2Fb[i][k])[_qp] + (1.0 - _dh[_qp]) * (*_prop_d2Fa[i][k])[_qp];
if (k_var == _eta_var)
return _dh[_qp] * (*_prop_d2Fb[i][j])[_qp] + (1.0 - _dh[_qp]) * (*_prop_d2Fa[i][j])[_qp];
return _h[_qp] * (*_prop_d3Fb[i][j][k])[_qp] + (1.0 - _h[_qp]) * (*_prop_d3Fa[i][j][k])[_qp];
}
Real
DerivativeMultiPhaseMaterial::computeD2F(unsigned int i_var, unsigned int j_var)
{
const unsigned int i = argIndex(i_var);
const int i_eta = _eta_index[i];
const unsigned int j = argIndex(j_var);
const int j_eta = _eta_index[j];
if (i_eta >= 0 && j_eta >= 0)
{
// if the derivatives are taken w.r.t. a single eta the d2hi term for eta_i appears, otherwise it drops out
// because we assume that hi _only_ depends on eta_i
Real d2F = (i_eta == j_eta) ? (*_d2hi[i_eta])[_qp] * (*_prop_Fi[i_eta])[_qp] : 0.0;
return d2F + _W * (*_d2g[i_eta][j_eta])[_qp];
}
if (i_eta >= 0)
return (*_dhi[i_eta])[_qp] * (*_prop_dFi[i_eta][j])[_qp];
if (j_eta >= 0)
return (*_dhi[j_eta])[_qp] * (*_prop_dFi[j_eta][i])[_qp];
Real d2F = 0.0;
for (unsigned n = 0; n < _num_fi; ++n)
d2F += (*_hi[n])[_qp] * (*_prop_d2Fi[n][i][j])[_qp];
return d2F;
}
Real
DerivativeMultiPhaseMaterial::computeD3F(unsigned int i_var, unsigned int j_var, unsigned int k_var)
{
const unsigned int i = argIndex(i_var);
const int i_eta = _eta_index[i];
const unsigned int j = argIndex(j_var);
const int j_eta = _eta_index[j];
const unsigned int k = argIndex(k_var);
const int k_eta = _eta_index[k];
// all arguments are eta-variables
if (i_eta >= 0 && j_eta >= 0 && k_eta >= 0)
{
// if the derivatives are taken w.r.t. a single eta the d3hi term for eta_i appears, otherwise it drops out
// because we assume that hi _only_ depends on eta_i
Real d3F = (i_eta == j_eta && j_eta == k_eta) ? (*_d3hi[i_eta])[_qp] * (*_prop_Fi[i_eta])[_qp] : 0.0;
return d3F + _W * (*_d3g[i_eta][j_eta][k_eta])[_qp];
}
// two arguments are eta-variables
if (i_eta >= 0 && j_eta >= 0)
return (i_eta == j_eta) ? (*_d2hi[i_eta])[_qp] * (*_prop_dFi[i_eta][k])[_qp] : 0.0;
if (j_eta >= 0 && k_eta >= 0)
return (j_eta == k_eta) ? (*_d2hi[j_eta])[_qp] * (*_prop_dFi[j_eta][i])[_qp] : 0.0;
if (k_eta >= 0 && i_eta >= 0)
return (k_eta == i_eta) ? (*_d2hi[k_eta])[_qp] * (*_prop_dFi[k_eta][j])[_qp] : 0.0;
// one argument is an eta-variable
if (i_eta >= 0)
return (*_dhi[i_eta])[_qp] * (*_prop_d2Fi[i_eta][j][k])[_qp];
if (j_eta >= 0)
return (*_dhi[j_eta])[_qp] * (*_prop_d2Fi[j_eta][i][k])[_qp];
if (k_eta >= 0)
return (*_dhi[k_eta])[_qp] * (*_prop_d2Fi[k_eta][i][j])[_qp];
// no arguments are eta-variables
Real d3F = 0.0;
for (unsigned n = 0; n < _num_fi; ++n)
d3F += (*_hi[n])[_qp] * (*_prop_d3Fi[n][i][j][k])[_qp];
return d3F;
}
Real
ElasticEnergyMaterial::computeDF(unsigned int i_var)
{
unsigned int i = argIndex(i_var);
// product rule d/di computeF (doubleContraction commutes)
return 0.5 * ((*_delasticity_tensor[i])[_qp] * _strain[_qp]).doubleContraction(_strain[_qp]) +
(_elasticity_tensor[_qp] * (*_dstrain[i])[_qp]).doubleContraction(_strain[_qp]);
}
Real
DerivativeTwoPhaseMaterial::computeDF(unsigned int i_var)
{
if (i_var == _eta_var)
return _dh[_qp] * (_prop_Fb[_qp] - _prop_Fa[_qp]) + _W * _dg[_qp];
else
{
unsigned int i = argIndex(i_var);
return _h[_qp] * (*_prop_dFb[i])[_qp] + (1.0 - _h[_qp]) * (*_prop_dFa[i])[_qp];
}
}
Real
ElasticEnergyMaterial::computeD2F(unsigned int i_var, unsigned int j_var)
{
unsigned int i = argIndex(i_var);
unsigned int j = argIndex(j_var);
// product rule d/dj computeDF
// TODO: simplify because doubleContraction commutes
return 0.5 * (((*_d2elasticity_tensor[i][j])[_qp] * _strain[_qp] +
(*_delasticity_tensor[i])[_qp] * (*_dstrain[j])[_qp] +
(*_delasticity_tensor[j])[_qp] * (*_dstrain[i])[_qp] +
_elasticity_tensor[_qp] * (*_d2strain[i][j])[_qp])
.doubleContraction(_strain[_qp]) +
((*_delasticity_tensor[i])[_qp] * _strain[_qp] +
_elasticity_tensor[_qp] * (*_dstrain[i])[_qp])
.doubleContraction((*_dstrain[j])[_qp])
+
( // dstress/dj
(*_delasticity_tensor[j])[_qp] * _strain[_qp] +
_elasticity_tensor[_qp] * (*_dstrain[j])[_qp])
.doubleContraction((*_dstrain[i])[_qp]) +
_stress[_qp].doubleContraction((*_d2strain[i][j])[_qp]));
}
Real
DerivativeMultiPhaseMaterial::computeDF(unsigned int i_var)
{
const unsigned int i = argIndex(i_var);
const int i_eta = _eta_index[i];
if (i_eta >= 0)
return (*_dhi[i_eta])[_qp] * (*_prop_Fi[i_eta])[_qp] + _W * (*_dg[i_eta])[_qp];
else
{
Real dF = 0.0;
for (unsigned n = 0; n < _num_fi; ++n)
dF += (*_hi[n])[_qp] * (*_prop_dFi[n][i])[_qp];
return dF;
}
}
DiscreteNucleation::DiscreteNucleation(const InputParameters & params)
: DerivativeFunctionMaterialBase(params),
_nvar(coupledComponents("op_names")),
_op_index(_nvar),
_op_values(getParam<std::vector<Real>>("op_values")),
_penalty(getParam<Real>("penalty")),
_penalty_mode(getParam<MooseEnum>("penalty_mode")),
_map(getUserObject<DiscreteNucleationMap>("map"))
{
// check inputs
if (_nvar != _op_values.size())
mooseError("The op_names and op_values parameter vectors must have the same number of entries");
if (_nvar != _args.size())
mooseError("Internal error.");
// get libMesh variable numbers
for (unsigned int i = 0; i < _nvar; ++i)
_op_index[i] = argIndex(coupled("op_names", i));
}
DiscreteNucleation::DiscreteNucleation(const InputParameters & params) :
DerivativeFunctionMaterialBase(params),
_nvar(coupledComponents("op_names")),
_op_index(_nvar),
_op_values(getParam<std::vector<Real> >("op_values")),
_penalty(getParam<Real>("penalty")),
_penalty_mode(getParam<MooseEnum>("penalty_mode")),
_map(getUserObject<DiscreteNucleationMap>("map"))
{
// check inputs
if (_nvar != _op_values.size())
mooseError("The op_names and op_values parameter vectors must have the same number of entries");
if (_nvar != _args.size())
mooseError("Internal error.");
// this does not work with legacy UO initialization
if (_fe_problem.legacyUoInitialization())
mooseError("DiscreteNucleation needs to be run with legacy UO initialization disabled. Set Problem/use_legacy_uo_initialization=false");
// get libMesh variable numbers
for (unsigned int i = 0; i < _nvar; ++i)
_op_index[i] = argIndex(coupled("op_names", i));
}
DerivativeMultiPhaseBase::DerivativeMultiPhaseBase(const InputParameters & parameters) :
DerivativeFunctionMaterialBase(parameters),
_eta_index(_nargs, -1),
_num_etas(coupledComponents("etas")),
_eta_names(_num_etas),
_eta_vars(_num_etas),
_fi_names(getParam<std::vector<MaterialPropertyName> >("fi_names")),
_num_fi(_fi_names.size()),
_prop_Fi(_num_fi),
_prop_dFi(_num_fi),
_prop_d2Fi(_num_fi),
_prop_d3Fi(_num_fi),
_hi_names(getParam<std::vector<MaterialPropertyName> >("hi_names")),
_num_hi(_hi_names.size()),
_hi(_num_hi),
_g(getMaterialProperty<Real>("g")),
_dg(_num_etas),
_d2g(_num_etas),
_d3g(_num_etas),
_W(getParam<Real>("W"))
{
// check passed in parameter vectors
if (_num_fi != _num_hi)
mooseError("Need to pass in as many hi_names as fi_names in DerivativeMultiPhaseBase " << name());
// get order parameter names and libmesh variable names, set barrier function derivatives
for (unsigned int i = 0; i < _num_etas; ++i)
{
_eta_names[i] = getVar("etas", i)->name();
_eta_vars[i] = coupled("etas", i);
// for each coupled variable we need to know if it was coupled through "etas"
// and - if so - which coupled component of "etas" it comes from
_eta_index[argIndex(_eta_vars[i])] = i;
// barrier function derivatives
_dg[i] = &getMaterialPropertyDerivative<Real>("g", _eta_names[i]);
_d2g[i].resize(_num_etas);
if (_third_derivatives)
_d3g[i].resize(_num_etas);
for (unsigned int j = 0; j < _num_etas; ++j)
{
_d2g[i][j] = &getMaterialPropertyDerivative<Real>("g", _eta_names[i], _eta_names[j]);
if (_third_derivatives)
{
_d3g[i][j].resize(_num_etas);
for (unsigned int k = 0; k < _num_etas; ++k)
_d3g[i][j][k] = &getMaterialPropertyDerivative<Real>("g", _eta_names[i], _eta_names[j], _eta_names[k]);
}
}
}
// reserve space and set phase material properties
for (unsigned int n = 0; n < _num_fi; ++n)
{
// get phase free energy
_prop_Fi[n] = &getMaterialPropertyByName<Real>(_fi_names[n]);
_prop_dFi[n].resize(_nargs);
_prop_d2Fi[n].resize(_nargs);
_prop_d3Fi[n].resize(_nargs);
// get switching function
_hi[n] = &getMaterialPropertyByName<Real>(_hi_names[n]);
for (unsigned int i = 0; i < _nargs; ++i)
{
_prop_dFi[n][i] = &getMaterialPropertyDerivative<Real>(_fi_names[n], _arg_names[i]);
_prop_d2Fi[n][i].resize(_nargs);
if (_third_derivatives)
_prop_d3Fi[n][i].resize(_nargs);
for (unsigned int j = 0; j < _nargs; ++j)
{
_prop_d2Fi[n][i][j] = &getMaterialPropertyDerivative<Real>(_fi_names[n], _arg_names[i], _arg_names[j]);
if (_third_derivatives) {
_prop_d3Fi[n][i][j].resize(_nargs);
for (unsigned int k = 0; k < _nargs; ++k)
_prop_d3Fi[n][i][j][k] = &getMaterialPropertyDerivative<Real>(_fi_names[n], _arg_names[i], _arg_names[j], _arg_names[k]);
}
}
}
}
}