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rAKA/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening_inline_impl.cc
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/**
* @file material_linear_isotropic_hardening_inline_impl.cc
*
* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Benjamin Paccaud <benjamin.paccaud@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Apr 07 2014
* @date last modification: Fri May 29 2015
*
* @brief Implementation of the inline functions of the material plasticity
*
* @section LICENSE
*
* Copyright (©) 2014, 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/>.
*
*/
#include "material_linear_isotropic_hardening.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
/// Infinitesimal deformations
template <UInt dim>
inline void MaterialLinearIsotropicHardening<dim>::computeStressOnQuad(
const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
Matrix<Real> & inelastic_strain,
const Matrix<Real> & previous_inelastic_strain, Real & iso_hardening,
const Real & previous_iso_hardening, const Real & sigma_th,
const Real & previous_sigma_th) {
Real delta_sigma_th = sigma_th - previous_sigma_th;
Matrix<Real> grad_delta_u(grad_u);
grad_delta_u -= previous_grad_u;
// Compute trial stress, sigma_tr
Matrix<Real> sigma_tr(dim, dim);
MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr,
delta_sigma_th);
sigma_tr += previous_sigma;
// We need a full stress tensor, otherwise the VM stress is messed up
Matrix<Real> sigma_tr_dev(3, 3, 0);
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
sigma_tr_dev(i, j) = sigma_tr(i, j);
sigma_tr_dev -= Matrix<Real>::eye(3, sigma_tr.trace() / 3.0);
// Compute effective deviatoric trial stress
Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
Real sigma_tr_dev_eff = std::sqrt(3. / 2. * s);
bool initial_yielding =
((sigma_tr_dev_eff - iso_hardening - this->sigma_y) > 0);
Real dp = (initial_yielding)
? (sigma_tr_dev_eff - this->sigma_y - previous_iso_hardening) /
(3 * this->mu + this->h)
: 0;
iso_hardening = previous_iso_hardening + this->h * dp;
// Compute inelastic strain (ignore last components in 1-2D)
Matrix<Real> delta_inelastic_strain(dim, dim, 0.);
if (std::abs(sigma_tr_dev_eff) >
sigma_tr_dev.norm<L_inf>() * Math::getTolerance()) {
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
delta_inelastic_strain(i, j) = sigma_tr_dev(i, j);
delta_inelastic_strain *= 3. / 2. * dp / sigma_tr_dev_eff;
}
MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
grad_delta_u, sigma, previous_sigma, inelastic_strain,
previous_inelastic_strain, delta_inelastic_strain);
}
/* -------------------------------------------------------------------------- */
/// Finite deformations
template <UInt dim>
inline void MaterialLinearIsotropicHardening<dim>::computeStressOnQuad(
const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
Matrix<Real> & inelastic_strain,
const Matrix<Real> & previous_inelastic_strain, Real & iso_hardening,
const Real & previous_iso_hardening, const Real & sigma_th,
const Real & previous_sigma_th, const Matrix<Real> & F_tensor) {
// Finite plasticity
Real dp = 0.0;
Real d_dp = 0.0;
UInt n = 0;
Real delta_sigma_th = sigma_th - previous_sigma_th;
Matrix<Real> grad_delta_u(grad_u);
grad_delta_u -= previous_grad_u;
// Compute trial stress, sigma_tr
Matrix<Real> sigma_tr(dim, dim);
MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr,
delta_sigma_th);
sigma_tr += previous_sigma;
// Compute deviatoric trial stress, sigma_tr_dev
Matrix<Real> sigma_tr_dev(sigma_tr);
sigma_tr_dev -= Matrix<Real>::eye(dim, sigma_tr.trace() / 3.0);
// Compute effective deviatoric trial stress
Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
Real sigma_tr_dev_eff = std::sqrt(3. / 2. * s);
// compute the cauchy stress to apply the Von-Mises criterion
Matrix<Real> cauchy_stress(dim, dim);
Material::computeCauchyStressOnQuad<dim>(F_tensor, sigma_tr, cauchy_stress);
Matrix<Real> cauchy_stress_dev(cauchy_stress);
cauchy_stress_dev -= Matrix<Real>::eye(dim, cauchy_stress.trace() / 3.0);
Real c = cauchy_stress_dev.doubleDot(cauchy_stress_dev);
Real cauchy_stress_dev_eff = std::sqrt(3. / 2. * c);
const Real iso_hardening_t = previous_iso_hardening;
iso_hardening = iso_hardening_t;
// Loop for correcting stress based on yield function
// F is written in terms of S
// bool initial_yielding = ( (sigma_tr_dev_eff - iso_hardening -
// this->sigma_y) > 0) ;
// while ( initial_yielding && std::abs(sigma_tr_dev_eff - iso_hardening -
// this->sigma_y) > Math::getTolerance() ) {
// d_dp = (sigma_tr_dev_eff - 3. * this->mu *dp - iso_hardening -
// this->sigma_y)
// / (3. * this->mu + this->h);
// //r = r + h * dp;
// dp = dp + d_dp;
// iso_hardening = iso_hardening_t + this->h * dp;
// ++n;
// /// TODO : explicit this criterion with an error message
// if ((std::abs(d_dp) < 1e-9) || (n>50)){
// AKANTU_DEBUG_INFO("convergence of increment of plastic strain. d_dp:"
// << d_dp << "\tNumber of iteration:"<<n);
// break;
// }
// }
// F is written in terms of cauchy stress
bool initial_yielding =
((cauchy_stress_dev_eff - iso_hardening - this->sigma_y) > 0);
while (initial_yielding &&
std::abs(cauchy_stress_dev_eff - iso_hardening - this->sigma_y) >
Math::getTolerance()) {
d_dp = (cauchy_stress_dev_eff - 3. * this->mu * dp - iso_hardening -
this->sigma_y) /
(3. * this->mu + this->h);
// r = r + h * dp;
dp = dp + d_dp;
iso_hardening = iso_hardening_t + this->h * dp;
++n;
/// TODO : explicit this criterion with an error message
if ((d_dp < 1e-5) || (n > 50)) {
AKANTU_DEBUG_INFO("convergence of increment of plastic strain. d_dp:"
<< d_dp << "\tNumber of iteration:" << n);
break;
}
}
// Update internal variable
Matrix<Real> delta_inelastic_strain(dim, dim, 0.);
if (std::abs(sigma_tr_dev_eff) >
sigma_tr_dev.norm<L_inf>() * Math::getTolerance()) {
// /// compute the direction of the plastic strain as \frac{\partial
// F}{\partial S} = \frac{3}{2J\sigma_{effective}}} Ft \sigma_{dev} F
Matrix<Real> cauchy_dev_F(dim, dim);
cauchy_dev_F.mul<false, false>(F_tensor, cauchy_stress_dev);
Real J = F_tensor.det();
Real constant = J ? 1. / J : 0;
constant *= 3. * dp / (2. * cauchy_stress_dev_eff);
delta_inelastic_strain.mul<true, false>(F_tensor, cauchy_dev_F, constant);
// Direction given by the piola kirchhoff deviatoric tensor \frac{\partial
// F}{\partial S} = \frac{3}{2\sigma_{effective}}}S_{dev}
// delta_inelastic_strain.copy(sigma_tr_dev);
// delta_inelastic_strain *= 3./2. * dp / sigma_tr_dev_eff;
}
MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
grad_delta_u, sigma, previous_sigma, inelastic_strain,
previous_inelastic_strain, delta_inelastic_strain);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialLinearIsotropicHardening<dim>::computeTangentModuliOnQuad(
Matrix<Real> & tangent, __attribute__((unused)) const Matrix<Real> & grad_u,
__attribute__((unused)) const Matrix<Real> & previous_grad_u,
__attribute__((unused)) const Matrix<Real> & sigma_tensor,
__attribute__((unused)) const Matrix<Real> & previous_sigma_tensor,
__attribute__((unused)) const Real & iso_hardening) const {
// Real r=iso_hardening;
// Matrix<Real> grad_delta_u(grad_u);
// grad_delta_u -= previous_grad_u;
// //Compute trial stress, sigma_tr
// Matrix<Real> sigma_tr(dim, dim);
// MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr);
// sigma_tr += previous_sigma_tensor;
// // Compute deviatoric trial stress, sigma_tr_dev
// Matrix<Real> sigma_tr_dev(sigma_tr);
// sigma_tr_dev -= Matrix<Real>::eye(dim, sigma_tr.trace() / 3.0);
// // Compute effective deviatoric trial stress
// Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
// Real sigma_tr_dev_eff=std::sqrt(3./2. * s);
// // Compute deviatoric stress, sigma_dev
// Matrix<Real> sigma_dev(sigma_tensor);
// sigma_dev -= Matrix<Real>::eye(dim, sigma_tensor.trace() / 3.0);
// // Compute effective deviatoric stress
// s = sigma_dev.doubleDot(sigma_dev);
// Real sigma_dev_eff = std::sqrt(3./2. * s);
// Real xr = 0.0;
// if(sigma_tr_dev_eff > sigma_dev_eff * Math::getTolerance())
// xr = sigma_dev_eff / sigma_tr_dev_eff;
// Real __attribute__((unused)) q = 1.5 * (1. / (1. + 3. * this->mu /
// this->h) - xr);
/*
UInt cols = tangent.cols();
UInt rows = tangent.rows();
for (UInt m = 0; m < rows; ++m) {
UInt i = VoigtHelper<dim>::vec[m][0];
UInt j = VoigtHelper<dim>::vec[m][1];
for (UInt n = 0; n < cols; ++n) {
UInt k = VoigtHelper<dim>::vec[n][0];
UInt l = VoigtHelper<dim>::vec[n][1];
*/
// This section of the code is commented
// There were some problems with the convergence of plastic-coupled
// simulations with thermal expansion
// XXX: DO NOT REMOVE
/*if (((sigma_tr_dev_eff-iso_hardening-sigmay) > 0) && (xr > 0)) {
tangent(m,n) =
2. * this->mu * q * (sigma_tr_dev (i,j) / sigma_tr_dev_eff) * (sigma_tr_dev
(k,l) / sigma_tr_dev_eff) +
(i==k) * (j==l) * 2. * this->mu * xr +
(i==j) * (k==l) * (this->kpa - 2./3. * this->mu * xr);
if ((m == n) && (m>=dim))
tangent(m, n) = tangent(m, n) - this->mu * xr;
} else {*/
/*
tangent(m,n) = (i==k) * (j==l) * 2. * this->mu +
(i==j) * (k==l) * this->lambda;
tangent(m,n) -= (m==n) * (m>=dim) * this->mu;
*/
//}
// correct tangent stiffness for shear component
//}
//}
MaterialElastic<dim>::computeTangentModuliOnQuad(tangent);
}
} // akantu
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