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rAKA/src/model/solid_mechanics/material_inline_impl.hh
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material_inline_impl.hh
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/**
* Copyright (©) 2010-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*/
/* -------------------------------------------------------------------------- */
#include "integration_point.hh"
#include "material.hh"
#include "solid_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
// #ifndef __AKANTU_MATERIAL_INLINE_IMPL_CC__
// #define __AKANTU_MATERIAL_INLINE_IMPL_CC__
namespace akantu {
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2>
constexpr inline void Material::gradUToF(const Eigen::MatrixBase<D1> & grad_u,
Eigen::MatrixBase<D2> & F) {
assert(F.size() >= grad_u.size() && grad_u.size() == dim * dim &&
"The dimension of the tensor F should be greater or "
"equal to the dimension of the tensor grad_u.");
F.setIdentity();
F.template block<dim, dim>(0, 0) += grad_u;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1>
constexpr inline decltype(auto)
Material::gradUToF(const Eigen::MatrixBase<D1> & grad_u) {
Matrix<Real, dim, dim> F;
gradUToF<dim>(grad_u, F);
return F;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2, typename D3>
constexpr inline void Material::StoCauchy(const Eigen::MatrixBase<D1> & F,
const Eigen::MatrixBase<D2> & S,
Eigen::MatrixBase<D3> & sigma,
const Real & C33) {
Real J = F.determinant() * std::sqrt(C33);
Matrix<Real, dim, dim> F_S;
F_S = F * S;
Real constant = (J < std::numeric_limits<Real>::epsilon()) ? 0. : 1. / J;
sigma = constant * F_S * F.transpose();
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2>
constexpr inline decltype(auto)
Material::StoCauchy(const Eigen::MatrixBase<D1> & F,
const Eigen::MatrixBase<D2> & S, const Real & C33) {
Matrix<Real, dim, dim> sigma;
Material::StoCauchy<dim>(F, S, sigma, C33);
return sigma;
}
/* -------------------------------------------------------------------------- */
template <typename D1, typename D2>
constexpr inline void Material::rightCauchy(const Eigen::MatrixBase<D1> & F,
Eigen::MatrixBase<D2> & C) {
C = F.transpose() * F;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D>
constexpr inline decltype(auto)
Material::rightCauchy(const Eigen::MatrixBase<D> & F) {
Matrix<Real, dim, dim> C;
rightCauchy(F, C);
return C;
}
/* -------------------------------------------------------------------------- */
template <typename D1, typename D2>
constexpr inline void Material::leftCauchy(const Eigen::MatrixBase<D1> & F,
Eigen::MatrixBase<D2> & B) {
B = F * F.transpose();
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D>
constexpr inline decltype(auto)
Material::leftCauchy(const Eigen::MatrixBase<D> & F) {
Matrix<Real, dim, dim> B;
rightCauchy(F, B);
return B;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2>
constexpr inline void
Material::gradUToEpsilon(const Eigen::MatrixBase<D1> & grad_u,
Eigen::MatrixBase<D2> & epsilon) {
epsilon = .5 * (grad_u.transpose() + grad_u);
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1>
inline decltype(auto) constexpr Material::gradUToEpsilon(
const Eigen::MatrixBase<D1> & grad_u) {
Matrix<Real, dim, dim> epsilon;
Material::gradUToEpsilon<dim>(grad_u, epsilon);
return epsilon;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2>
constexpr inline void Material::gradUToE(const Eigen::MatrixBase<D1> & grad_u,
Eigen::MatrixBase<D2> & E) {
E = (grad_u.transpose() * grad_u + grad_u.transpose() + grad_u) / 2.;
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1>
constexpr inline decltype(auto)
Material::gradUToE(const Eigen::MatrixBase<D1> & grad_u) {
Matrix<Real, dim, dim> E;
gradUToE<dim>(grad_u, E);
return E;
}
/* -------------------------------------------------------------------------- */
template <typename D1>
inline Real Material::stressToVonMises(const Eigen::MatrixBase<D1> & stress) {
// compute deviatoric stress
auto dim = stress.cols();
auto && deviatoric_stress =
stress - Matrix<Real>::Identity(dim, dim) * stress.trace() / 3.;
// return Von Mises stress
return std::sqrt(3. * deviatoric_stress.doubleDot(deviatoric_stress) / 2.);
}
/* -------------------------------------------------------------------------- */
template <Int dim, typename D1, typename D2>
constexpr inline void
Material::setCauchyStressMatrix(const Eigen::MatrixBase<D1> & S_t,
Eigen::MatrixBase<D2> & sigma) {
sigma.zero();
/// see Finite ekement formulations for large deformation dynamic analysis,
/// Bathe et al. IJNME vol 9, 1975, page 364 ^t \f$\tau\f$
for (Int i = 0; i < dim; ++i) {
for (Int m = 0; m < dim; ++m) {
for (Int n = 0; n < dim; ++n) {
sigma(i * dim + m, i * dim + n) = S_t(m, n);
}
}
}
}
/* -------------------------------------------------------------------------- */
inline Int Material::getNbData(const Array<Element> & elements,
const SynchronizationTag & tag) const {
if (tag == SynchronizationTag::_smm_stress) {
return (this->isFiniteDeformation() ? 3 : 1) * spatial_dimension *
spatial_dimension * Int(sizeof(Real)) *
this->getModel().getNbIntegrationPoints(elements);
}
if (tag == SynchronizationTag::_smm_gradu) {
return spatial_dimension * spatial_dimension * Int(sizeof(Real)) *
this->getModel().getNbIntegrationPoints(elements);
}
return 0;
}
/* -------------------------------------------------------------------------- */
inline void Material::packData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) const {
if (tag == SynchronizationTag::_smm_stress) {
if (this->isFiniteDeformation()) {
packInternalFieldHelper(*piola_kirchhoff_2, buffer, elements);
packInternalFieldHelper(gradu, buffer, elements);
}
packInternalFieldHelper(stress, buffer, elements);
}
if (tag == SynchronizationTag::_smm_gradu) {
packInternalFieldHelper(gradu, buffer, elements);
}
}
/* -------------------------------------------------------------------------- */
inline void Material::unpackData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) {
if (tag == SynchronizationTag::_smm_stress) {
if (this->isFiniteDeformation()) {
unpackInternalFieldHelper(*piola_kirchhoff_2, buffer, elements);
unpackInternalFieldHelper(gradu, buffer, elements);
}
unpackInternalFieldHelper(stress, buffer, elements);
}
if (tag == SynchronizationTag::_smm_gradu) {
unpackInternalFieldHelper(gradu, buffer, elements);
}
}
} // namespace akantu
// #endif /* __AKANTU_MATERIAL_INLINE_IMPL_CC__ */
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