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material_elastic_inline_impl.hh
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material_elastic_inline_impl.hh
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/**
* @file material_elastic_inline_impl.hh
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Thu Feb 20 2020
*
* @brief Implementation of the inline functions of the material elastic
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* 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 "material_elastic.hh"
/* -------------------------------------------------------------------------- */
// #ifndef __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__
// #define __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__
namespace akantu {
/* -------------------------------------------------------------------------- */
template <Int dim>
template <typename Args>
inline void MaterialElastic<dim>::computeStressOnQuad(Args && args) const {
auto && sigma = args["sigma"_n];
auto && grad_u = args["grad_u"_n];
Real sigma_th = 0.;
if constexpr (named_tuple_t<Args>::has("sigma_th"_n)) {
sigma_th = args["sigma_th"_n];
}
Real trace = grad_u.trace(); // trace = (\nabla u)_{kk}
// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
// u_{ij} + \nabla u_{ji})
sigma = 2. * mu * Material::gradUToEpsilon<dim>(grad_u) +
(lambda * trace + sigma_th) * Matrix<Real, dim, dim>::Identity();
}
/* -------------------------------------------------------------------------- */
template <>
template <typename Args>
inline void MaterialElastic<1>::computeStressOnQuad(Args && args) const {
auto && sigma = args["sigma"_n];
auto && grad_u = args["grad_u"_n];
Real sigma_th = 0.;
if constexpr (std::decay_t<Args>::has("sigma_th"_n)) {
sigma_th = args["sigma_th"_n];
}
sigma(0, 0) = this->E * grad_u(0, 0) + sigma_th;
}
/* -------------------------------------------------------------------------- */
template <Int dim>
template <typename Args>
inline void
MaterialElastic<dim>::computeTangentModuliOnQuad(Args && args) const {
auto && tangent = args["tangent_moduli"_n];
tangent.zero();
constexpr auto n = Material::getTangentStiffnessVoigtSize(dim);
// Real Ep = E/((1+nu)*(1-2*nu));
if constexpr (dim == 1) {
tangent(0, 0) = this->E;
return;
}
auto Miiii = lambda + 2 * mu;
[[maybe_unused]] auto Miijj = lambda;
[[maybe_unused]] auto Mijij = mu;
tangent(0, 0) = Miiii;
// test of dimension should by optimized out by the compiler due to the
// template
if constexpr (dim >= 2) {
tangent(1, 1) = Miiii;
tangent(0, 1) = Miijj;
tangent(1, 0) = Miijj;
tangent(n - 1, n - 1) = Mijij;
}
if constexpr (dim == 3) {
tangent(2, 2) = Miiii;
tangent(0, 2) = Miijj;
tangent(1, 2) = Miijj;
tangent(2, 0) = Miijj;
tangent(2, 1) = Miijj;
tangent(3, 3) = Mijij;
tangent(4, 4) = Mijij;
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
template <class Args>
inline void MaterialElastic<dim>::computePotentialEnergyOnQuad(Args && args,
Real & epot) {
epot = .5 * args["sigma"_n].doubleDot(args["grad_u"_n]);
}
} // namespace akantu
// #endif /* __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__ */

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