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rAKA/src/model/solid_mechanics/materials/material_elastic_orthotropic.cc
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material_elastic_orthotropic.cc
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/**
* @file material_elastic_orthotropic.cc
*
* @author Till Junge <till.junge@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Thu Oct 15 2015
*
* @brief Orthotropic elastic material
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 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_orthotropic.hh"
#include "solid_mechanics_model.hh"
#include <algorithm>
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt Dim>
MaterialElasticOrthotropic<Dim>::MaterialElasticOrthotropic(
SolidMechanicsModel & model, const ID & id)
: MaterialElasticLinearAnisotropic<Dim>(model, id) {
AKANTU_DEBUG_IN();
this->registerParam("E1", E1, Real(0.), _pat_parsmod, "Young's modulus (n1)");
this->registerParam("E2", E2, Real(0.), _pat_parsmod, "Young's modulus (n2)");
this->registerParam("nu12", nu12, Real(0.), _pat_parsmod,
"Poisson's ratio (12)");
this->registerParam("G12", G12, Real(0.), _pat_parsmod, "Shear modulus (12)");
if (Dim > 2) {
this->registerParam("E3", E3, Real(0.), _pat_parsmod,
"Young's modulus (n3)");
this->registerParam("nu13", nu13, Real(0.), _pat_parsmod,
"Poisson's ratio (13)");
this->registerParam("nu23", nu23, Real(0.), _pat_parsmod,
"Poisson's ratio (23)");
this->registerParam("G13", G13, Real(0.), _pat_parsmod,
"Shear modulus (13)");
this->registerParam("G23", G23, Real(0.), _pat_parsmod,
"Shear modulus (23)");
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt Dim> void MaterialElasticOrthotropic<Dim>::initMaterial() {
AKANTU_DEBUG_IN();
Material::initMaterial();
updateInternalParameters();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
inline Real vector_norm(Vector<Real> & vec) {
Real norm = 0;
for (UInt i = 0; i < vec.size(); ++i) {
norm += vec(i) * vec(i);
}
return std::sqrt(norm);
}
/* -------------------------------------------------------------------------- */
template <UInt Dim>
void MaterialElasticOrthotropic<Dim>::updateInternalParameters() {
/* 1) construction of temporary material frame stiffness tensor------------ */
// http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real nu31 = nu13 * E3 / E1;
Real nu32 = nu23 * E3 / E2;
// Full (i.e. dim^2 by dim^2) stiffness tensor in material frame
if (Dim == 1) {
AKANTU_DEBUG_ERROR("Dimensions 1 not implemented: makes no sense to have "
"orthotropy for 1D");
}
Real Gamma;
if (Dim == 3)
Gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
2 * nu21 * nu32 * nu13);
if (Dim == 2)
Gamma = 1 / (1 - nu12 * nu21);
// Lamé's first parameters
this->Cprime(0, 0) = E1 * (1 - nu23 * nu32) * Gamma;
this->Cprime(1, 1) = E2 * (1 - nu13 * nu31) * Gamma;
if (Dim == 3)
this->Cprime(2, 2) = E3 * (1 - nu12 * nu21) * Gamma;
// normalised poisson's ratio's
this->Cprime(1, 0) = this->Cprime(0, 1) = E1 * (nu21 + nu31 * nu23) * Gamma;
if (Dim == 3) {
this->Cprime(2, 0) = this->Cprime(0, 2) = E1 * (nu31 + nu21 * nu32) * Gamma;
this->Cprime(2, 1) = this->Cprime(1, 2) = E2 * (nu32 + nu12 * nu31) * Gamma;
}
// Lamé's second parameters (shear moduli)
if (Dim == 3) {
this->Cprime(3, 3) = G23;
this->Cprime(4, 4) = G13;
this->Cprime(5, 5) = G12;
} else
this->Cprime(2, 2) = G12;
/* 1) rotation of C into the global frame */
this->rotateCprime();
this->C.eig(this->eigC);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialElasticOrthotropic<dim>::computePotentialEnergyOnQuad(
const Matrix<Real> & grad_u, const Matrix<Real> & sigma, Real & epot) {
epot = .5 * sigma.doubleDot(grad_u);
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialElasticOrthotropic<spatial_dimension>::computePotentialEnergy(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Material::computePotentialEnergy(el_type, ghost_type);
AKANTU_DEBUG_ASSERT(!this->finite_deformation,
"finite deformation not possible in material orthotropic "
"(TO BE IMPLEMENTED)");
if (ghost_type != _not_ghost)
return;
Array<Real>::scalar_iterator epot =
this->potential_energy(el_type, ghost_type).begin();
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
computePotentialEnergyOnQuad(grad_u, sigma, *epot);
++epot;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialElasticOrthotropic<spatial_dimension>::
computePotentialEnergyByElement(ElementType type, UInt index,
Vector<Real> & epot_on_quad_points) {
AKANTU_DEBUG_ASSERT(!this->finite_deformation,
"finite deformation not possible in material orthotropic "
"(TO BE IMPLEMENTED)");
Array<Real>::matrix_iterator gradu_it =
this->gradu(type).begin(spatial_dimension, spatial_dimension);
Array<Real>::matrix_iterator gradu_end =
this->gradu(type).begin(spatial_dimension, spatial_dimension);
Array<Real>::matrix_iterator stress_it =
this->stress(type).begin(spatial_dimension, spatial_dimension);
UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
gradu_it += index * nb_quadrature_points;
gradu_end += (index + 1) * nb_quadrature_points;
stress_it += index * nb_quadrature_points;
Real * epot_quad = epot_on_quad_points.storage();
Matrix<Real> grad_u(spatial_dimension, spatial_dimension);
for (; gradu_it != gradu_end; ++gradu_it, ++stress_it, ++epot_quad) {
grad_u.copy(*gradu_it);
computePotentialEnergyOnQuad(grad_u, *stress_it, *epot_quad);
}
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(elastic_orthotropic, MaterialElasticOrthotropic);
} // akantu
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