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rAKA/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.cc
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material_elastic_linear_anisotropic.cc
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/**
* @file material_elastic_linear_anisotropic.cc
*
* @author Till Junge <till.junge@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Sep 25 2013
* @date last modification: Thu Oct 15 2015
*
* @brief Anisotropic elastic material
*
* @section LICENSE
*
* Copyright (©) 2014, 2015 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 <UInt 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), alpha(0), was_stiffness_assembled(false) {
AKANTU_DEBUG_IN();
this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
(*this->dir_vecs.back())[0] = 1.;
this->registerParam("n1", *(this->dir_vecs.back()), _pat_parsmod,
"Direction of main material axis");
if (dim > 1) {
this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
(*this->dir_vecs.back())[1] = 1.;
this->registerParam("n2", *(this->dir_vecs.back()), _pat_parsmod,
"Direction of secondary material axis");
}
if (dim > 2) {
this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
(*this->dir_vecs.back())[2] = 1.;
this->registerParam("n3", *(this->dir_vecs.back()), _pat_parsmod,
"Direction of tertiary material axis");
}
for (UInt i = 0; i < voigt_h::size; ++i) {
UInt start = 0;
if (this->symmetric) {
start = i;
}
for (UInt j = start; j < voigt_h::size; ++j) {
std::stringstream param("C");
param << "C" << i + 1 << j + 1;
this->registerParam(param.str(), this->Cprime(i, j), Real(0.),
_pat_parsmod, "Coefficient " + param.str());
}
}
this->registerParam("alpha", this->alpha, _pat_parsmod,
"Proportion of viscous stress");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim> void MaterialElasticLinearAnisotropic<dim>::initMaterial() {
AKANTU_DEBUG_IN();
Material::initMaterial();
updateInternalParameters();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialElasticLinearAnisotropic<dim>::updateInternalParameters() {
Material::updateInternalParameters();
if (this->symmetric) {
for (UInt i = 0; i < voigt_h::size; ++i) {
for (UInt j = i + 1; j < voigt_h::size; ++j) {
this->Cprime(j, i) = this->Cprime(i, j);
}
}
}
this->rotateCprime();
this->C.eig(this->eigC);
this->was_stiffness_assembled = false;
}
/* -------------------------------------------------------------------------- */
template <UInt Dim> void MaterialElasticLinearAnisotropic<Dim>::rotateCprime() {
// start by filling the empty parts fo Cprime
UInt diff = Dim * Dim - voigt_h::size;
for (UInt i = voigt_h::size; i < Dim * Dim; ++i) {
for (UInt j = 0; j < Dim * Dim; ++j) {
this->Cprime(i, j) = this->Cprime(i - diff, j);
}
}
for (UInt i = 0; i < Dim * Dim; ++i) {
for (UInt j = voigt_h::size; j < Dim * Dim; ++j) {
this->Cprime(i, j) = this->Cprime(i, j - diff);
}
}
// construction of rotator tensor
// normalise rotation matrix
for (UInt j = 0; j < Dim; ++j) {
Vector<Real> rot_vec = this->rot_mat(j);
rot_vec = *this->dir_vecs[j];
rot_vec.normalize();
}
// make sure the vectors form a right-handed base
Vector<Real> test_axis(3);
Vector<Real> v1(3), v2(3), v3(3);
if (Dim == 2) {
for (UInt i = 0; i < Dim; ++i) {
v1[i] = this->rot_mat(0, i);
v2[i] = this->rot_mat(1, i);
v3[i] = 0.;
}
v3[2] = 1.;
v1[2] = 0.;
v2[2] = 0.;
} else if (Dim == 3) {
v1 = this->rot_mat(0);
v2 = this->rot_mat(1);
v3 = this->rot_mat(2);
}
test_axis.crossProduct(v1, v2);
test_axis -= v3;
if (test_axis.norm() > 8 * std::numeric_limits<Real>::epsilon()) {
AKANTU_DEBUG_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.norm() << ".");
}
// create the rotator and the reverse rotator
Matrix<Real> rotator(Dim * Dim, Dim * Dim);
Matrix<Real> revrotor(Dim * Dim, Dim * Dim);
for (UInt i = 0; i < Dim; ++i) {
for (UInt j = 0; j < Dim; ++j) {
for (UInt k = 0; k < Dim; ++k) {
for (UInt l = 0; l < Dim; ++l) {
UInt I = voigt_h::mat[i][j];
UInt 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> Cfull(Dim * Dim, Dim * Dim);
Cfull = rotator * Cprime * revrotor;
for (UInt i = 0; i < voigt_h::size; ++i) {
for (UInt j = 0; j < voigt_h::size; ++j) {
this->C(i, j) = Cfull(i, j);
}
}
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialElasticLinearAnisotropic<dim>::computeStress(
ElementType el_type, GhostType ghost_type) {
// Wikipedia convention:
// 2*eps_ij (i!=j) = voigt_eps_I
// http://en.wikipedia.org/wiki/Voigt_notation
AKANTU_DEBUG_IN();
Array<Real>::iterator<Matrix<Real>> gradu_it =
this->gradu(el_type, ghost_type).begin(dim, dim);
Array<Real>::iterator<Matrix<Real>> gradu_end =
this->gradu(el_type, ghost_type).end(dim, dim);
UInt nb_quad_pts = gradu_end - gradu_it;
// create array for strains and stresses of all dof of all gauss points
// for efficient computation of stress
Matrix<Real> voigt_strains(voigt_h::size, nb_quad_pts);
Matrix<Real> voigt_stresses(voigt_h::size, nb_quad_pts);
// copy strains
Matrix<Real> strain(dim, dim);
for (UInt q = 0; gradu_it != gradu_end; ++gradu_it, ++q) {
Matrix<Real> & grad_u = *gradu_it;
for (UInt I = 0; I < voigt_h::size; ++I) {
Real voigt_factor = voigt_h::factors[I];
UInt i = voigt_h::vec[I][0];
UInt j = voigt_h::vec[I][1];
voigt_strains(I, q) = voigt_factor * (grad_u(i, j) + grad_u(j, i)) / 2.;
}
}
// compute the strain rate proportional part if needed
// bool viscous = this->alpha == 0.; // only works if default value
bool viscous = false;
if (viscous) {
Array<Real> strain_rate(0, dim * dim, "strain_rate");
Array<Real> & velocity = this->model.getVelocity();
const Array<UInt> & elem_filter = this->element_filter(el_type, ghost_type);
this->fem.gradientOnIntegrationPoints(velocity, strain_rate, dim, el_type,
ghost_type, elem_filter);
Array<Real>::matrix_iterator gradu_dot_it = strain_rate.begin(dim, dim);
Array<Real>::matrix_iterator gradu_dot_end = strain_rate.end(dim, dim);
Matrix<Real> strain_dot(dim, dim);
for (UInt q = 0; gradu_dot_it != gradu_dot_end; ++gradu_dot_it, ++q) {
Matrix<Real> & grad_u_dot = *gradu_dot_it;
for (UInt I = 0; I < voigt_h::size; ++I) {
Real voigt_factor = voigt_h::factors[I];
UInt i = voigt_h::vec[I][0];
UInt j = voigt_h::vec[I][1];
voigt_strains(I, q) = this->alpha * voigt_factor *
(grad_u_dot(i, j) + grad_u_dot(j, i)) / 2.;
}
}
}
// compute stresses
voigt_stresses = this->C * voigt_strains;
// copy stresses back
Array<Real>::iterator<Matrix<Real>> stress_it =
this->stress(el_type, ghost_type).begin(dim, dim);
Array<Real>::iterator<Matrix<Real>> stress_end =
this->stress(el_type, ghost_type).end(dim, dim);
for (UInt q = 0; stress_it != stress_end; ++stress_it, ++q) {
Matrix<Real> & stress = *stress_it;
for (UInt I = 0; I < voigt_h::size; ++I) {
UInt i = voigt_h::vec[I][0];
UInt j = voigt_h::vec[I][1];
stress(i, j) = stress(j, i) = voigt_stresses(I, q);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialElasticLinearAnisotropic<dim>::computeTangentModuli(
const ElementType & el_type, Array<Real> & tangent_matrix,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
tangent.copy(this->C);
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;
this->was_stiffness_assembled = true;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real MaterialElasticLinearAnisotropic<dim>::getCelerity(
__attribute__((unused)) const Element & element) const {
return std::sqrt(this->eigC(0) / rho);
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(elastic_anisotropic, MaterialElasticLinearAnisotropic);
} // akantu
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