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rAKA/examples/new_material/local_material_damage_inline_impl.cc
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local_material_damage_inline_impl.cc
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/**
* @file local_material_damage_inline_impl.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Aug 10 2015
*
* @brief Implementation of the inline functions of the material damage
*
* @section LICENSE
*
* Copyright (©) 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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
inline void LocalMaterialDamage::computeStressOnQuad(Matrix<Real> & grad_u,
Matrix<Real> & sigma,
Real & dam) {
Real trace = grad_u.trace();
/// \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));
}
}
Real Y = 0;
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
Y += sigma(i, j) * grad_u(i, j);
}
}
Y *= 0.5;
Real Fd = Y - Yd - Sd * dam;
if (Fd > 0)
dam = (Y - Yd) / Sd;
dam = std::min(dam, 1.);
sigma *= 1 - dam;
}
/* -------------------------------------------------------------------------- */
inline void LocalMaterialDamage::computePotentialEnergyOnQuad(
Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & epot) {
epot = 0.;
for (UInt i = 0, t = 0; i < spatial_dimension; ++i)
for (UInt j = 0; j < spatial_dimension; ++j, ++t)
epot += sigma(i, j) * (grad_u(i, j) - (i == j));
epot *= .5;
}
/* -------------------------------------------------------------------------- */
inline Real LocalMaterialDamage::getCelerity(__attribute__((unused))
const Element & element) const {
// Here the fastest celerity is the push wave speed
return (std::sqrt((2 * mu + lambda) / rho));
}
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