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rAKA/model/solid_mechanics/materials/material_damage_inline_impl.cc
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material_damage_inline_impl.cc
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/**
* @file material_damage_inline_impl.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Chambart <marion.chambart@epfl.ch>
* @date Tue Jul 27 11:57:43 2010
*
* @brief Implementation of the inline functions of the material damage
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 MaterialDamage::computeStress(Real * F, Real * sigma, Real & dam) {
Real trace = F[0] + F[4] + F[8]; /// \F_{11} + \F_{22} + \F_{33}
/// \sigma_{ij} = \lamda * \F_{kk} * \delta_{ij} + 2 * \mu * \F_{ij}
sigma[0] = lambda * trace + 2*mu*F[0];
sigma[4] = lambda * trace + 2*mu*F[4];
sigma[8] = lambda * trace + 2*mu*F[8];
sigma[1] = sigma[3] = mu * (F[1] + F[3]);
sigma[2] = sigma[6] = mu * (F[2] + F[6]);
sigma[5] = sigma[7] = mu * (F[5] + F[7]);
Real Y =
sigma[0]*F[0] +
sigma[1]*F[1] +
sigma[2]*F[2] +
sigma[3]*F[3] +
sigma[4]*F[4] +
sigma[5]*F[5] +
sigma[6]*F[6] +
sigma[7]*F[7] +
sigma[8]*F[8];
Y *= 0.5;
Real Fd = Y - Yd - Sd*dam;
if (Fd > 0) dam = (Y - Yd) / Sd;
dam = std::min(dam,1.);
sigma[0] *= 1-dam;
sigma[4] *= 1-dam;
sigma[8] *= 1-dam;
sigma[1] *= 1-dam;
sigma[3] *= 1-dam;
sigma[2] *= 1-dam;
sigma[6] *= 1-dam;
sigma[5] *= 1-dam;
sigma[7] *= 1-dam;
}
/* -------------------------------------------------------------------------- */
inline void MaterialDamage::computePotentialEnergy(Real * F, 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[t] * (F[t] - (i == j));
*epot *= .5;
}
/* -------------------------------------------------------------------------- */
inline Real MaterialDamage::celerity() {
return sqrt(E/rho);
}
/* -------------------------------------------------------------------------- */
inline Real MaterialDamage::getStableTimeStep(Real h) {
return (h/celerity());
}
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