void
CappedDruckerPragerCosseratStressUpdate::consistentTangentOperator(
const RankTwoTensor & /*stress_trial*/,
Real /*p_trial*/,
Real /*q_trial*/,
const RankTwoTensor & stress,
Real /*p*/,
Real q,
Real gaE,
const yieldAndFlow & smoothed_q,
const RankFourTensor & Eijkl,
bool compute_full_tangent_operator,
RankFourTensor & cto) const
{
if (!compute_full_tangent_operator)
{
cto = Eijkl;
return;
}
RankFourTensor EAijkl;
for (unsigned i = 0; i < _tensor_dimensionality; ++i)
for (unsigned j = 0; j < _tensor_dimensionality; ++j)
for (unsigned k = 0; k < _tensor_dimensionality; ++k)
for (unsigned l = 0; l < _tensor_dimensionality; ++l)
{
cto(i, j, k, l) = 0.5 * (Eijkl(i, j, k, l) + Eijkl(j, i, k, l));
EAijkl(i, j, k, l) = 0.5 * (Eijkl(i, j, k, l) - Eijkl(j, i, k, l));
}
const RankTwoTensor s_over_q =
(q == 0.0 ? RankTwoTensor()
: (0.5 * (stress + stress.transpose()) -
stress.trace() * RankTwoTensor(RankTwoTensor::initIdentity) / 3.0) /
q);
const RankTwoTensor E_s_over_q = Eijkl.innerProductTranspose(s_over_q); // not symmetric in kl
const RankTwoTensor Ekl =
RankTwoTensor(RankTwoTensor::initIdentity).initialContraction(Eijkl); // symmetric in kl
for (unsigned i = 0; i < _tensor_dimensionality; ++i)
for (unsigned j = 0; j < _tensor_dimensionality; ++j)
for (unsigned k = 0; k < _tensor_dimensionality; ++k)
for (unsigned l = 0; l < _tensor_dimensionality; ++l)
{
cto(i, j, k, l) -= (i == j) * (1.0 / 3.0) *
(Ekl(k, l) * (1.0 - _dp_dpt) + 0.5 * E_s_over_q(k, l) * (-_dp_dqt));
cto(i, j, k, l) -=
s_over_q(i, j) * (Ekl(k, l) * (-_dq_dpt) + 0.5 * E_s_over_q(k, l) * (1.0 - _dq_dqt));
}
if (smoothed_q.dg[1] != 0.0)
{
const RankFourTensor Tijab = _Ehost * (gaE / _Epp) * smoothed_q.dg[1] * d2qdstress2(stress);
RankFourTensor inv = RankFourTensor(RankFourTensor::initIdentitySymmetricFour) + Tijab;
try
{
inv = inv.transposeMajor().invSymm();
}
catch (const MooseException & e)
{
// Cannot form the inverse, so probably at some degenerate place in stress space.
// Just return with the "best estimate" of the cto.
mooseWarning("CappedDruckerPragerCosseratStressUpdate: Cannot invert 1+T in consistent "
"tangent operator computation at quadpoint ",
_qp,
" of element ",
_current_elem->id());
return;
}
cto = (cto.transposeMajor() * inv).transposeMajor();
}
cto += EAijkl;
}
