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isotropic_hardening.cpp
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Mon, Jul 1, 09:19

isotropic_hardening.cpp
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/**
* @file
* LICENSE
*
* Copyright (©) 2016-2021 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "isotropic_hardening.hh"
#include "influence.hh"
/* -------------------------------------------------------------------------- */
namespace tamaas {
/* -------------------------------------------------------------------------- */
template <model_type type>
IsotropicHardening<type>::IsotropicHardening(Model* model, Real sigma_0, Real h)
: Material<type>(model), sigma_0(sigma_0), h(h) {
plastic_strain =
allocateGrid<type, false, Real>(model->getDiscretization(), trait::voigt);
cumulated_plastic_strain =
allocateGrid<type, false, Real>(model->getDiscretization(), 1);
plastic_strain.initialize();
cumulated_plastic_strain.initialize();
model->registerField("plastic_strain", plastic_strain);
model->registerField("cumulated_plastic_strain", cumulated_plastic_strain);
}
/* -------------------------------------------------------------------------- */
template <>
void IsotropicHardening<model_type::volume_2d>::
computeInelasticDeformationIncrement(Field& increment, const Field& strain,
const Field& strain_increment) {
influence::ElasticHelper<dim> elasticity(this->model->getShearModulus(),
this->model->getPoissonRatio());
plastic_strain.reset();
cumulated_plastic_strain.reset();
Loop::loop(
[&elasticity,
this](auto dep, // < plastic strain increment
auto epsilon, // < total strain
auto delta_epsilon, // < strain increment
auto ep, // < plastic strain
Real& p // < cumulated plastic strain
) {
// Trial elastic stress
auto sigma_tr = elasticity(epsilon - ep + delta_epsilon);
// Zero increment by default
dep = 0;
// Deviatoric trial stress
decltype(sigma_tr) dev;
dev.deviatoric(sigma_tr);
// Von-Mises stress
Real von_mises = std::sqrt(1.5) * dev.l2norm();
// Plasticity condition
if (von_mises - this->hardening(p) > 0) {
// radial return
Real dp = (von_mises - this->hardening(p)) / (3 * elasticity.mu + h);
dev *= 3 * dp / (2 * von_mises); // saving memory (dev is delta ep)
dep = dev;
p += dp;
ep += dep;
}
},
range<Mat>(increment), range<CMat>(strain), range<CMat>(strain_increment),
range<Mat>(*plastic_strain), *cumulated_plastic_strain);
}
/* -------------------------------------------------------------------------- */
template <>
void IsotropicHardening<model_type::volume_2d>::computeStress(
Field& stress, const Field& strain, const Field& strain_increment) {
this->computeInelasticDeformationIncrement(stress, strain, strain_increment);
const influence::ElasticHelper<dim> elasticity(
this->model->getShearModulus(), this->model->getPoissonRatio());
Loop::loop(
[&elasticity](auto sigma, // < stress
auto epsilon, // < total strain
auto delta_epsilon, // < strain increment
auto ep // < plastic strain
) {
sigma = epsilon;
sigma += delta_epsilon;
sigma -= ep;
sigma = elasticity(sigma);
},
range<Mat>(stress), range<CMat>(strain), range<CMat>(strain_increment),
range<CMat>(*plastic_strain));
}
/* -------------------------------------------------------------------------- */
template <model_type type>
void IsotropicHardening<type>::update() {
plastic_strain.update();
cumulated_plastic_strain.update();
}
/* -------------------------------------------------------------------------- */
template <>
void IsotropicHardening<model_type::volume_2d>::applyTangentIncrement(
Grid<Real, dim>& output, const Grid<Real, dim>& input,
const Grid<Real, dim>& strain,
const Grid<Real, dim>& strain_increment) const {
const influence::ElasticHelper<dim> elasticity(
this->model->getShearModulus(), this->model->getPoissonRatio());
Loop::loop(
[&elasticity, this](auto out, auto in, auto epsilon, auto delta_epsilon,
auto ep, const Real& p) {
auto sigma_tr = elasticity(epsilon - ep + delta_epsilon);
decltype(sigma_tr) dev;
dev.deviatoric(sigma_tr, 3);
auto von_mises = std::sqrt(1.5) * dev.l2norm();
if (von_mises - this->hardening(p) > 0) {
Real dp = (von_mises - this->hardening(p)) / (3 * elasticity.mu + h);
// Applying tangent from Bonnet & Frangi, p.175
const Real beta = 3 * elasticity.mu * dp / von_mises;
const Real gamma = 3 * elasticity.mu / (3 * elasticity.mu + this->h);
const Real dot = dev.dot(in);
dev *= 3 * elasticity.mu * (gamma - beta) * dot /
(von_mises * von_mises);
out.deviatoric(in);
out *= 2 * elasticity.mu * beta;
out += dev;
} else
out = 0;
},
range<Mat>(output), range<CMat>(input), range<CMat>(strain),
range<CMat>(strain_increment), range<CMat>(*this->plastic_strain),
*this->cumulated_plastic_strain);
}
/* -------------------------------------------------------------------------- */
/* Template instanciation */
/* -------------------------------------------------------------------------- */
template class IsotropicHardening<model_type::volume_2d>;
} // namespace tamaas

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