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material_elastic_linear_anisotropic.cc
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/**
* @file material_elastic_linear_anisotropic.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Till Junge <till.junge@epfl.ch>
* @author Enrico Milanese <enrico.milanese@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Sep 25 2013
* @date last modification: Fri Jul 24 2020
*
* @brief Anisotropic elastic material
*
*
* @section LICENSE
*
* Copyright (©) 2014-2021 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_linear_anisotropic.hh"
#include "solid_mechanics_model.hh"
#include <algorithm>
#include <sstream>
namespace akantu {
/* -------------------------------------------------------------------------- */
template <Int dim>
MaterialElasticLinearAnisotropic<dim>::MaterialElasticLinearAnisotropic(
SolidMechanicsModel & model, const ID & id, bool symmetric)
: Material(model, id), rot_mat(dim, dim), Cprime(dim * dim, dim * dim),
C(voigt_h::size, voigt_h::size), eigC(voigt_h::size),
symmetric(symmetric), was_stiffness_assembled(false) {
AKANTU_DEBUG_IN();
for (int i : arange(dim)) {
this->dir_vecs.emplace_back(std::make_unique<Vector<Real, dim>>());
auto && n = *this->dir_vecs.back();
n.zero();
n[i] = 1.;
this->registerParam("n" + std::to_string(i + 1), *(this->dir_vecs.back()),
_pat_parsmod, "Direction of main material axis");
}
for (auto i : arange(voigt_h::size)) {
decltype(i) start = 0;
if (this->symmetric) {
start = i;
}
for (auto j : arange(start, voigt_h::size)) {
auto param = "C" + std::to_string(i + 1) + std::to_string(j + 1);
this->registerParam(param, this->Cprime(i, j), Real(0.), _pat_parsmod,
"Coefficient " + param);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <Int dim> void MaterialElasticLinearAnisotropic<dim>::initMaterial() {
AKANTU_DEBUG_IN();
Material::initMaterial();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialElasticLinearAnisotropic<dim>::updateInternalParameters() {
Material::updateInternalParameters();
if (this->symmetric) {
for (auto i : arange(voigt_h::size)) {
for (auto j : arange(i + 1, voigt_h::size)) {
this->Cprime(j, i) = this->Cprime(i, j);
}
}
}
this->rotateCprime();
this->C.eig(this->eigC);
this->was_stiffness_assembled = false;
}
/* -------------------------------------------------------------------------- */
template <Int Dim> void MaterialElasticLinearAnisotropic<Dim>::rotateCprime() {
// start by filling the empty parts fo Cprime
auto diff = Dim * Dim - voigt_h::size;
for (auto i : arange(voigt_h::size, Dim * Dim)) {
for (auto j : arange(Dim * Dim)) {
this->Cprime(i, j) = this->Cprime(i - diff, j);
}
}
for (auto i : arange(Dim * Dim)) {
for (auto j : arange(voigt_h::size, Dim * Dim)) {
this->Cprime(i, j) = this->Cprime(i, j - diff);
}
}
// construction of rotator tensor
// normalise rotation matrix
for (auto j : arange(Dim)) {
auto && rot_vec = this->rot_mat(j);
rot_vec = *this->dir_vecs[j];
rot_vec.normalize();
}
// make sure the vectors form a right-handed base
Real test_axis = 0.;
if (Dim == 2) {
Vector<Real, 3> v1 = Vector<Real, 3>::Zero();
Vector<Real, 3> v2 = Vector<Real, 3>::Zero();
v1.block<Dim, 1>(0, 0) = this->rot_mat(0);
v2.block<Dim, 1>(0, 0) = this->rot_mat(1);
Vector<Real, 3> v3 = v1.cross(v2);
if (v3.norm() < 8 * std::numeric_limits<Real>::epsilon()) {
AKANTU_ERROR("The axis vectors parallel.");
}
v3.normalize();
test_axis = (v1.cross(v2) - v3).norm();
} else if (Dim == 3) {
Vector<Real, 3> v1 = this->rot_mat(0);
Vector<Real, 3> v2 = this->rot_mat(1);
Vector<Real, 3> v3 = this->rot_mat(2);
test_axis = (v1.cross(v2) - v3).norm();
}
if (test_axis > 8 * std::numeric_limits<Real>::epsilon()) {
AKANTU_ERROR("The axis vectors do not form a right-handed coordinate "
<< "system. I. e., ||n1 x n2 - n3|| should be zero, but "
<< "it is " << test_axis << ".");
}
// create the rotator and the reverse rotator
Matrix<Real, Dim * Dim, Dim * Dim> rotator;
Matrix<Real, Dim * Dim, Dim * Dim> revrotor;
for (auto i : arange(Dim)) {
for (auto j : arange(Dim)) {
for (auto k : arange(Dim)) {
for (auto l : arange(Dim)) {
auto I = voigt_h::mat[i][j];
auto J = voigt_h::mat[k][l];
rotator(I, J) = this->rot_mat(k, i) * this->rot_mat(l, j);
revrotor(I, J) = this->rot_mat(i, k) * this->rot_mat(j, l);
}
}
}
}
// create the full rotated matrix
Matrix<Real, Dim * Dim, Dim * Dim> Cfull(Dim * Dim, Dim * Dim);
Cfull = rotator * Cprime * revrotor;
for (auto i : arange(voigt_h::size)) {
for (auto j : arange(voigt_h::size)) {
this->C(i, j) = Cfull(i, j);
}
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialElasticLinearAnisotropic<dim>::computeStress(
ElementType el_type, GhostType ghost_type) {
auto && arguments = getArguments(el_type, ghost_type);
for (auto && data : arguments) {
this->computeStressOnQuad(data);
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialElasticLinearAnisotropic<dim>::computeTangentModuli(
ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
auto && arguments =
Material::getArgumentsTangent<dim>(tangent_matrix, el_type, ghost_type);
for (auto && args : arguments) {
this->computeTangentModuliOnQuad(args);
}
this->was_stiffness_assembled = true;
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialElasticLinearAnisotropic<dim>::computePotentialEnergy(
ElementType el_type) {
AKANTU_DEBUG_ASSERT(!this->finite_deformation,
"finite deformation not possible in material anisotropic "
"(TO BE IMPLEMENTED)");
auto && arguments = Material::getArguments<dim>(el_type, _not_ghost);
for (auto && args :
zip(arguments, this->potential_energy(el_type, _not_ghost))) {
this->computePotentialEnergyOnQuad(std::get<0>(args), std::get<1>(args));
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialElasticLinearAnisotropic<dim>::computePotentialEnergyByElement(
ElementType type, Int index, Vector<Real> & epot_on_quad_points) {
auto gradu_view = make_view<dim, dim>(this->gradu(type));
auto stress_view = make_view<dim, dim>(this->stress(type));
auto nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
auto gradu_it = gradu_view.begin() + index * nb_quadrature_points;
auto gradu_end = gradu_it + nb_quadrature_points;
auto stress_it = stress_view.begin() + index * nb_quadrature_points;
auto stress_end = stress_it + nb_quadrature_points;
auto epot_quad = epot_on_quad_points.begin();
Matrix<Real> grad_u(dim, dim);
for (auto data : zip("grad_u"_n = range(gradu_it, gradu_end),
"sigma"_n = range(stress_it, stress_end),
"Epot"_n = epot_on_quad_points)) {
this->computePotentialEnergyOnQuad(data, data["Epot"_n]);
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
Real MaterialElasticLinearAnisotropic<dim>::getCelerity(
const Element & /*element*/) const {
return std::sqrt(this->eigC(0) / rho);
}
/* -------------------------------------------------------------------------- */
template class MaterialElasticLinearAnisotropic<1>;
template class MaterialElasticLinearAnisotropic<2>;
template class MaterialElasticLinearAnisotropic<3>;
static bool material_is_alocated_elastic =
instantiateMaterial<MaterialElasticLinearAnisotropic>(
"elastic_anisotropic");
} // namespace akantu

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