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rAKA/src/model/solid_mechanics/materials/material_damage/material_mazars_inline_impl.hh
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material_mazars_inline_impl.hh
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/**
* @file material_mazars_inline_impl.hh
*
* @author Marion Estelle Chambart <mchambart@stucky.ch>
* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Apr 06 2011
* @date last modification: Wed Feb 03 2016
*
* @brief Implementation of the inline functions of the material damage
*
*
* Copyright (©) 2010-2018 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_mazars.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
inline void MaterialMazars<spatial_dimension>::computeStressOnQuad(
const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
Real & Ehat) {
Matrix<Real> epsilon(3, 3);
epsilon.zero();
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
}
}
Vector<Real> Fdiag(3);
Math::matrixEig(3, epsilon.storage(), Fdiag.storage());
Ehat = 0.;
for (UInt i = 0; i < 3; ++i) {
Real epsilon_p = std::max(Real(0.), Fdiag(i));
Ehat += epsilon_p * epsilon_p;
}
Ehat = sqrt(Ehat);
MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);
if (damage_in_compute_stress) {
computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
}
if (not this->is_non_local) {
computeDamageAndStressOnQuad(grad_u, sigma, dam, Ehat);
}
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
inline void MaterialMazars<spatial_dimension>::computeDamageAndStressOnQuad(
const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
Real & Ehat) {
if (!damage_in_compute_stress) {
Vector<Real> Fdiag(3);
Fdiag.zero();
Matrix<Real> epsilon(3, 3);
epsilon.zero();
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
}
}
Math::matrixEig(3, epsilon.storage(), Fdiag.storage());
computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
}
sigma *= 1 - dam;
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
inline void MaterialMazars<spatial_dimension>::computeDamageOnQuad(
const Real & epsilon_equ,
__attribute__((unused)) const Matrix<Real> & sigma,
const Vector<Real> & epsilon_princ, Real & dam) {
Real Fs = epsilon_equ - K0;
if (Fs > 0.) {
Real dam_t;
Real dam_c;
dam_t =
1 - K0 * (1 - At) / epsilon_equ - At * (exp(-Bt * (epsilon_equ - K0)));
dam_c =
1 - K0 * (1 - Ac) / epsilon_equ - Ac * (exp(-Bc * (epsilon_equ - K0)));
Real Cdiag;
Cdiag = this->E * (1 - this->nu) / ((1 + this->nu) * (1 - 2 * this->nu));
Vector<Real> sigma_princ(3);
sigma_princ(0) = Cdiag * epsilon_princ(0) +
this->lambda * (epsilon_princ(1) + epsilon_princ(2));
sigma_princ(1) = Cdiag * epsilon_princ(1) +
this->lambda * (epsilon_princ(0) + epsilon_princ(2));
sigma_princ(2) = Cdiag * epsilon_princ(2) +
this->lambda * (epsilon_princ(1) + epsilon_princ(0));
Vector<Real> sigma_p(3);
for (UInt i = 0; i < 3; i++) {
sigma_p(i) = std::max(Real(0.), sigma_princ(i));
}
// sigma_p *= 1. - dam;
Real trace_p = this->nu / this->E * (sigma_p(0) + sigma_p(1) + sigma_p(2));
Real alpha_t = 0;
for (UInt i = 0; i < 3; ++i) {
Real epsilon_t = (1 + this->nu) / this->E * sigma_p(i) - trace_p;
Real epsilon_p = std::max(Real(0.), epsilon_princ(i));
alpha_t += epsilon_t * epsilon_p;
}
alpha_t /= epsilon_equ * epsilon_equ;
alpha_t = std::min(alpha_t, Real(1.));
Real alpha_c = 1. - alpha_t;
alpha_t = std::pow(alpha_t, beta);
alpha_c = std::pow(alpha_c, beta);
Real damtemp;
damtemp = alpha_t * dam_t + alpha_c * dam_c;
dam = std::max(damtemp, dam);
dam = std::min(dam, Real(1.));
}
}
/* -------------------------------------------------------------------------- */
// template<UInt spatial_dimension>
// inline void
// MaterialMazars<spatial_dimension>::computeTangentModuliOnQuad(Matrix<Real> &
// tangent) {
// MaterialElastic<spatial_dimension>::computeTangentModuliOnQuad(tangent);
// tangent *= (1-dam);
// }
} // namespace akantu
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