bool
FlowRateModel::computeDflowrateDstress(RankTwoTensor & dflowrate_dstress,
const RankTwoTensor & pk2,
const RankTwoTensor & ce,
const std::vector<Real> & internal_var,
const unsigned int start_index,
const unsigned int /*size*/) const
{
RankTwoTensor pk2_dev = computePK2Deviatoric(pk2, ce);
Real eqv_stress = computeEqvStress(pk2_dev, ce);
Real sigy = _flow_stress_uo.value(internal_var[start_index]);
Real dflowrate_dseqv = _ref_flow_rate * _flow_rate_exponent * std::pow(eqv_stress/sigy,_flow_rate_exponent-1) * 1/sigy;
if (dflowrate_dseqv > _flow_rate_tol)
{
#ifdef DEBUG
mooseWarning("dflowrate_dseqv greater than " << _flow_rate_tol << " " << dflowrate_dseqv << " " << eqv_stress << " " << sigy );
#endif
return false;
}
RankTwoTensor tau = pk2_dev * ce;
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > 0)
dseqv_dpk2dev = 3/(2 * eqv_stress) * tau * ce;
RankTwoTensor ce_inv = ce.inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i==k && j==l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * ce(k, l)/3.0;
}
dflowrate_dstress = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
return true;
}
bool
stzRHEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp, const std::string & coupled_var_name, RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real dflowrate_dseqv;
if (eqv_stress>_strength[qp])
// dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
(1.0/(_grain_pressure*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
dflowrate_dseqv = _v*std::exp(-1/_chiv[qp])*(1.0-1.0/(eqv_stress*eqv_stress));
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > _strength[qp])
dseqv_dpk2dev = 1.5/eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i==k && j==l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l)/3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}
bool
HEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp,
const std::string & coupled_var_name,
RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real dflowrate_dseqv = _ref_flow_rate * _flow_rate_exponent *
std::pow(eqv_stress / _strength[qp], _flow_rate_exponent - 1.0) /
_strength[qp];
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > 0.0)
dseqv_dpk2dev = 1.5 / eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i == k && j == l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l) / 3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}
bool
stznewHEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp, const std::string & coupled_var_name, RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
// Real s_xx = _tensor[qp](0,0);
// Real s_yy = _tensor[qp](1,1);
// Real tau_xy= _tensor[qp](0,1);
// Real s_mean = 1.0/3.0*(s_xx+s_yy);
// Real PI = 3.1415926;
// Real tau_max = std::pow((s_xx-s_yy)/2*(s_xx-s_yy)/2+tau_xy*tau_xy,0.5);
// Real eqv_stress = tau_max ;
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real _pressure_eff=_grain_pressure-_biot*_pf[qp];
// Real _t_taunew = _agrain[qp]/std::sqrt(_grain_pressure/_rho);
Real _t_taunew = _agrain[qp]/std::sqrt(_pressure_eff/_rho);
// Real dflowrate_dseqv = _ref_flow_rate * _flow_rate_exponent * std::pow(eqv_stress/_strength[qp],_flow_rate_exponent-1.0)/_strength[qp];
// stz
// Real dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
// (1/(_grain_pressure*_chiv[qp])*(1-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress))*(eqv_stress>_strength[qp]);
//
Real dflowrate_dseqv;
if (eqv_stress>_strength[qp])
// dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
(1.0/(_grain_pressure*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
// Original Stuff
{
dflowrate_dseqv = 1/_t_taunew*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_pressure_eff/_chiv[qp])* \
(1.0/(_pressure_eff*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
} // Modified
// {
//dflowrate_dseqv = 1.0/_t_taunew*std::exp(-1.0/_chiv[qp])*(-1.0*_strength[qp])/(eqv_stress*eqv_stress);
// } // dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chi)*std::exp(eqv_stress/_grain_pressure/_chi)* \
// (1.0/(_grain_pressure*_chi)*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > _strength[qp])
dseqv_dpk2dev = 1.5/eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i==k && j==l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l)/3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}