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material_standard_linear_solid_deviatoric.cc
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material_standard_linear_solid_deviatoric.cc
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/**
* @file material_standard_linear_solid_deviatoric.cc
*
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Vladislav Yastrebov <vladislav.yastrebov@epfl.ch>
*
* @date creation: Wed May 04 2011
* @date last modification: Fri Apr 09 2021
*
* @brief Material Visco-elastic
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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_standard_linear_solid_deviatoric.hh"
#include "solid_mechanics_model.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <Int dim>
MaterialStandardLinearSolidDeviatoric<
dim>::MaterialStandardLinearSolidDeviatoric(SolidMechanicsModel & model,
const ID & id)
: MaterialElastic<dim>(model, id), stress_dev("stress_dev", *this),
history_integral("history_integral", *this),
dissipated_energy("dissipated_energy", *this) {
AKANTU_DEBUG_IN();
this->registerParam("Eta", eta, Real(1.), _pat_parsable | _pat_modifiable,
"Viscosity");
this->registerParam("Ev", Ev, Real(1.), _pat_parsable | _pat_modifiable,
"Stiffness of the viscous element");
this->registerParam("Einf", E_inf, Real(1.), _pat_readable,
"Stiffness of the elastic element");
UInt stress_size = dim * dim;
this->stress_dev.initialize(stress_size);
this->history_integral.initialize(stress_size);
this->dissipated_energy.initialize(1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialStandardLinearSolidDeviatoric<dim>::initMaterial() {
AKANTU_DEBUG_IN();
updateInternalParameters();
MaterialElastic<dim>::initMaterial();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialStandardLinearSolidDeviatoric<dim>::updateInternalParameters() {
MaterialElastic<dim>::updateInternalParameters();
E_inf = this->E - this->Ev;
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialStandardLinearSolidDeviatoric<dim>::setToSteadyState(
ElementType el_type, GhostType ghost_type) {
/// Loop on all quadrature points
for (auto && args : this->getArguments(el_type, ghost_type)) {
const auto & grad_u = tuple::get<"grad_u"_h>(args);
auto & dev_s = tuple::get<"sigma_dev"_h>(args);
auto & h = tuple::get<"history"_h>(args);
/// Compute the first invariant of strain
Real Theta = grad_u.trace();
dev_s = 2 * this->mu *
((grad_u + grad_u.transpose()) / 2. -
Theta * Matrix<Real, dim, dim>::Identity() / 3.);
h.zero();
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialStandardLinearSolidDeviatoric<dim>::computeStress(
ElementType el_type, GhostType ghost_type) {
Real tau = eta / Ev;
Real dt = this->model.getTimeStep();
Real exp_dt_tau = exp(-dt / tau);
Real exp_dt_tau_2 = exp(-.5 * dt / tau);
Matrix<Real, dim, dim> s;
Matrix<Real, dim, dim> epsilon_d;
/// Loop on all quadrature points
for (auto && args : this->getArguments(el_type, ghost_type)) {
const auto & grad_u = tuple::get<"grad_u"_h>(args);
auto & sigma = tuple::get<"sigma"_h>(args);
auto & dev_s = tuple::get<"sigma_dev"_h>(args);
auto & h = tuple::get<"history"_h>(args);
s.zero();
sigma.zero();
/// Compute the first invariant of strain
auto gamma_inf = E_inf / this->E;
auto gamma_v = Ev / this->E;
epsilon_d = this->template gradUToEpsilon<dim>(grad_u);
auto Theta = epsilon_d.trace();
epsilon_d -= Matrix<Real, dim, dim>::Identity() * epsilon_d.trace() / 3.;
Matrix<Real, dim, dim> U_rond_prim =
Matrix<Real, dim, dim>::Identity() * gamma_inf * this->kpa * Theta;
s = this->mu * epsilon_d;
h = exp_dt_tau * h + exp_dt_tau_2 * (s - dev_s);
dev_s = s;
sigma = U_rond_prim + gamma_inf * s + gamma_v * h;
}
this->updateDissipatedEnergy(el_type, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <Int dim>
void MaterialStandardLinearSolidDeviatoric<dim>::updateDissipatedEnergy(
ElementType el_type, GhostType ghost_type) {
Real tau = eta / Ev;
Matrix<Real, dim, dim> q;
Matrix<Real, dim, dim> q_rate;
Matrix<Real, dim, dim> epsilon_d;
auto dt = this->model.getTimeStep();
auto gamma_v = Ev / this->E;
auto alpha = 1. / (2. * this->mu * gamma_v);
for (auto && data : zip(this->getArguments(el_type, ghost_type),
dissipated_energy(el_type, ghost_type))) {
auto && args = std::get<0>(data);
auto & dis_energy = std::get<1>(data);
const auto & grad_u = tuple::get<"grad_u"_h>(args);
auto & sigma = tuple::get<"sigma"_h>(args);
auto & dev_s = tuple::get<"sigma_dev"_h>(args);
auto & h = tuple::get<"history"_h>(args);
/// Compute the first invariant of strain
epsilon_d = Material::gradUToEpsilon<dim>(grad_u);
auto Theta = epsilon_d.trace();
epsilon_d -= Matrix<Real, dim, dim>::Identity() * Theta / 3.;
q = (dev_s - h) * gamma_v;
q_rate = (dev_s * gamma_v - q) / tau;
dis_energy += ((epsilon_d - alpha * q) * q_rate * dt).sum();
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy() const {
AKANTU_DEBUG_IN();
Real de = 0.;
/// integrate the dissipated energy for each type of elements
for (const auto & type : this->element_filter.elementTypes(dim, _not_ghost)) {
de +=
this->fem.integrate(dissipated_energy(type, _not_ghost), type,
_not_ghost, this->element_filter(type, _not_ghost));
}
AKANTU_DEBUG_OUT();
return de;
}
/* -------------------------------------------------------------------------- */
template <Int dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy(
const Element & element) const {
AKANTU_DEBUG_IN();
auto nb_quadrature_points = this->fem.getNbIntegrationPoints(element.type);
auto it = this->dissipated_energy(element.type, _not_ghost)
.begin(nb_quadrature_points);
auto gindex = this->element_filter(element);
AKANTU_DEBUG_OUT();
return this->fem.integrate(it[element.element], element);
}
/* -------------------------------------------------------------------------- */
template <Int dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getEnergy(
const std::string & type) {
if (type == "dissipated") {
return getDissipatedEnergy();
}
if (type == "dissipated_sls_deviatoric") {
return getDissipatedEnergy();
}
return MaterialElastic<dim>::getEnergy(type);
}
/* -------------------------------------------------------------------------- */
template <Int dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getEnergy(
const std::string & energy_id, const Element & element) {
if (energy_id == "dissipated") {
return getDissipatedEnergy(element);
}
if (energy_id == "dissipated_sls_deviatoric") {
return getDissipatedEnergy(element);
}
return Parent::getEnergy(energy_id, element);
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(sls_deviatoric, MaterialStandardLinearSolidDeviatoric);
} // namespace akantu

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