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muSpectre/src/materials/stress_transformations_Kirchhoff_impl.hh
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stress_transformations_Kirchhoff_impl.hh
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/**
* @file stress_transformations_Kirchhoff_impl.hh
*
* @author Till Junge <till.junge@altermail.ch>
*
* @date 29 Oct 2018
*
* @brief Implementation of stress conversions for Kirchhoff stress
*
* Copyright © 2018 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with µSpectre; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#ifndef SRC_MATERIALS_STRESS_TRANSFORMATIONS_KIRCHHOFF_IMPL_HH_
#define SRC_MATERIALS_STRESS_TRANSFORMATIONS_KIRCHHOFF_IMPL_HH_
namespace muSpectre {
namespace MatTB {
namespace internal {
/* ----------------------------------------------------------------------
*/
/**
* Specialisation for the case where we get Kirchhoff stress (τ)
*/
template <Dim_t Dim, StrainMeasure StrainM>
struct PK1_stress<Dim, StressMeasure::Kirchhoff, StrainM>
: public PK1_stress<Dim, StressMeasure::no_stress_,
StrainMeasure::no_strain_> {
//! returns the converted stress
template <class Strain_t, class Stress_t>
inline static decltype(auto) compute(Strain_t && F, Stress_t && tau) {
return tau * F.inverse().transpose();
}
};
/* ----------------------------------------------------------------------
*/
/**
* Specialisation for the case where we get Kirchhoff stress (τ) derived
* with respect to Gradient
*/
template <Dim_t Dim>
struct PK1_stress<Dim, StressMeasure::Kirchhoff, StrainMeasure::Gradient>
: public PK1_stress<Dim, StressMeasure::Kirchhoff,
StrainMeasure::no_strain_> {
//! short-hand
using Parent = PK1_stress<Dim, StressMeasure::Kirchhoff,
StrainMeasure::no_strain_>;
using Parent::compute;
//! returns the converted stress and stiffness
template <class Strain_t, class Stress_t, class Tangent_t>
inline static decltype(auto) compute(Strain_t && F, Stress_t && tau,
Tangent_t && C) {
using T4_t = T4Mat<Real, Dim>;
using Mat_t = Eigen::Matrix<Real, Dim, Dim>;
Mat_t F_inv{F.inverse()};
T4_t increment{T4_t::Zero()};
for (int i{0}; i < Dim; ++i) {
const int k{i};
for (int j{0}; j < Dim; ++j) {
const int a{j};
for (int l{0}; l < Dim; ++l) {
get(increment, i, j, k, l) -= tau(a, l);
}
}
}
T4_t Ka{C + increment};
T4_t Kb{T4_t::Zero()};
for (int i{0}; i < Dim; ++i) {
for (int j{0}; j < Dim; ++j) {
for (int k{0}; k < Dim; ++k) {
for (int l{0}; l < Dim; ++l) {
for (int a{0}; a < Dim; ++a) {
for (int b{0}; b < Dim; ++b) {
get(Kb, j, i, k, l) +=
F_inv(i, a) * get(Ka, a, j, k, b) * F_inv(l, b);
}
}
}
}
}
}
Mat_t P = tau * F_inv.transpose();
return std::make_tuple(std::move(P), std::move(Kb));
}
};
} // namespace internal
} // namespace MatTB
} // namespace muSpectre
#endif // SRC_MATERIALS_STRESS_TRANSFORMATIONS_KIRCHHOFF_IMPL_HH_
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