RankFourTensor
TensorMechanicsPlasticMeanCapTC::consistentTangentOperator(const RankTwoTensor & trial_stress, Real intnl_old, const RankTwoTensor & stress, Real intnl,
const RankFourTensor & E_ijkl, const std::vector<Real> & cumulative_pm) const
{
if (!_use_custom_cto)
return TensorMechanicsPlasticModel::consistentTangentOperator(trial_stress, intnl_old, stress, intnl, E_ijkl, cumulative_pm);
Real df_dq;
Real alpha;
if (trial_stress.trace() >= tensile_strength(intnl_old))
{
df_dq = -dtensile_strength(intnl);
alpha = 1.0;
}
else
{
df_dq = dcompressive_strength(intnl);
alpha = -1.0;
}
RankTwoTensor elas;
for (unsigned int i = 0; i < 3; ++i)
for (unsigned int j = 0; j < 3; ++j)
for (unsigned int k = 0; k < 3; ++k)
elas(i, j) += E_ijkl(i, j, k, k);
const Real hw = -df_dq + alpha * elas.trace();
return E_ijkl - alpha / hw * elas.outerProduct(elas);
}
RankFourTensor
TensorMechanicsPlasticJ2::consistentTangentOperator(const RankTwoTensor & trial_stress,
Real intnl_old,
const RankTwoTensor & stress,
Real intnl,
const RankFourTensor & E_ijkl,
const std::vector<Real> & cumulative_pm) const
{
if (!_use_custom_cto)
return TensorMechanicsPlasticModel::consistentTangentOperator(
trial_stress, intnl_old, stress, intnl, E_ijkl, cumulative_pm);
Real mu = E_ijkl(0, 1, 0, 1);
Real h = 3 * mu + dyieldStrength(intnl);
RankTwoTensor sij = stress.deviatoric();
Real sII = stress.secondInvariant();
Real equivalent_stress = std::sqrt(3.0 * sII);
Real zeta = cumulative_pm[0] / (1.0 + 3.0 * mu * cumulative_pm[0] / equivalent_stress);
return E_ijkl - 3.0 * mu * mu / sII / h * sij.outerProduct(sij) -
4.0 * mu * mu * zeta * dflowPotential_dstress(stress, intnl);
}
