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rAKA/src/model/solid_mechanics/materials/material_elastic_inline_impl.cc
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material_elastic_inline_impl.cc
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/**
* @file material_elastic_inline_impl.cc
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Mon Apr 07 2014
*
* @brief Implementation of the inline functions of the material elastic
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void MaterialElastic<spatial_dimension>::computeStressOnQuad(const Matrix<Real> & grad_u,
Matrix<Real> & sigma,
const Real sigma_th) const {
Real trace = grad_u.trace(); // trace = (\nabla u)_{kk}
// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla u_{ij} + \nabla u_{ji})
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
sigma(i, j) = (i == j)*lambda*trace + mu*(grad_u(i, j) + grad_u(j, i)) + (i == j) * sigma_th;
}
}
}
/* -------------------------------------------------------------------------- */
template<>
inline void MaterialElastic<1>::computeStressOnQuad(const Matrix<Real> & grad_u,
Matrix<Real> & sigma,
Real sigma_th) const {
sigma(0, 0) = this->E * grad_u(0, 0) + sigma_th;
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void MaterialElastic<spatial_dimension>::computeTangentModuliOnQuad(Matrix<Real> & tangent) const {
UInt n = tangent.cols();
//Real Ep = E/((1+nu)*(1-2*nu));
Real Miiii = lambda + 2*mu;
Real Miijj = lambda;
Real Mijij = mu;
if(spatial_dimension == 1)
tangent(0, 0) = this->E;
else
tangent(0, 0) = Miiii;
// test of dimension should by optimized out by the compiler due to the template
if(spatial_dimension >= 2) {
tangent(1, 1) = Miiii;
tangent(0, 1) = Miijj;
tangent(1, 0) = Miijj;
tangent(n - 1, n - 1) = Mijij;
}
if(spatial_dimension == 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<UInt dim>
inline void MaterialElastic<dim>::computePotentialEnergyOnQuad(const Matrix<Real> & grad_u,
const Matrix<Real> & sigma,
Real & epot) {
epot = .5 * sigma.doubleDot(grad_u);
}
/* -------------------------------------------------------------------------- */
template<>
inline void MaterialElastic<1>::computeTangentModuliOnQuad(Matrix<Real> & tangent) const {
tangent(0, 0) = E;
}
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