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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: Tue Feb 20 2018
*
* @brief Material Visco-elastic
*
*
* 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_standard_linear_solid_deviatoric.hh"
#include "solid_mechanics_model.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt 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 <UInt dim>
void MaterialStandardLinearSolidDeviatoric<dim>::initMaterial() {
AKANTU_DEBUG_IN();
updateInternalParameters();
MaterialElastic<dim>::initMaterial();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialStandardLinearSolidDeviatoric<dim>::updateInternalParameters() {
MaterialElastic<dim>::updateInternalParameters();
E_inf = this->E - this->Ev;
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialStandardLinearSolidDeviatoric<dim>::setToSteadyState(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
Array<Real> & history_int_vect = history_integral(el_type, ghost_type);
Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);
/// Loop on all quadrature points
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
Matrix<Real> & dev_s = *stress_d;
Matrix<Real> & h = *history_int;
/// Compute the first invariant of strain
Real Theta = grad_u.trace();
for (UInt i = 0; i < dim; ++i) {
for (UInt j = 0; j < dim; ++j) {
dev_s(i, j) = 2 * this->mu *
(.5 * (grad_u(i, j) + grad_u(j, i)) -
1. / 3. * Theta * Math::kronecker(i, j));
h(i, j) = 0.;
}
}
/// Save the deviator of stress
++stress_d;
++history_int;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialStandardLinearSolidDeviatoric<dim>::computeStress(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Real tau = 0.;
// if(std::abs(Ev) > std::numeric_limits<Real>::epsilon())
tau = eta / Ev;
Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
Array<Real> & history_int_vect = history_integral(el_type, ghost_type);
Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);
Matrix<Real> s(dim, dim);
Real dt = this->model.getTimeStep();
Real exp_dt_tau = exp(-dt / tau);
Real exp_dt_tau_2 = exp(-.5 * dt / tau);
Matrix<Real> epsilon_v(dim, dim);
/// Loop on all quadrature points
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
Matrix<Real> & dev_s = *stress_d;
Matrix<Real> & h = *history_int;
s.zero();
sigma.zero();
/// Compute the first invariant of strain
Real gamma_inf = E_inf / this->E;
Real gamma_v = Ev / this->E;
auto epsilon_d = this->template gradUToEpsilon<dim>(grad_u);
Real Theta = epsilon_d.trace();
epsilon_v.eye(Theta / Real(3.));
epsilon_d -= epsilon_v;
Matrix<Real> U_rond_prim(dim, dim);
U_rond_prim.eye(gamma_inf * this->kpa * Theta);
for (UInt i = 0; i < dim; ++i) {
for (UInt j = 0; j < dim; ++j) {
s(i, j) = 2 * this->mu * epsilon_d(i, j);
h(i, j) = exp_dt_tau * h(i, j) + exp_dt_tau_2 * (s(i, j) - dev_s(i, j));
dev_s(i, j) = s(i, j);
sigma(i, j) = U_rond_prim(i, j) + gamma_inf * s(i, j) + gamma_v * h(i, j);
}
}
/// Save the deviator of stress
++stress_d;
++history_int;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
this->updateDissipatedEnergy(el_type, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialStandardLinearSolidDeviatoric<dim>::updateDissipatedEnergy(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
// if(ghost_type == _ghost) return 0.;
Real tau = 0.;
tau = eta / Ev;
Real * dis_energy = dissipated_energy(el_type, ghost_type).storage();
Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
Array<Real> & history_int_vect = history_integral(el_type, ghost_type);
Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);
Matrix<Real> q(dim, dim);
Matrix<Real> q_rate(dim, dim);
Matrix<Real> epsilon_d(dim, dim);
Matrix<Real> epsilon_v(dim, dim);
Real dt = this->model.getTimeStep();
Real gamma_v = Ev / this->E;
Real alpha = 1. / (2. * this->mu * gamma_v);
/// Loop on all quadrature points
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
Matrix<Real> & dev_s = *stress_d;
Matrix<Real> & h = *history_int;
/// Compute the first invariant of strain
this->template gradUToEpsilon<dim>(grad_u, epsilon_d);
Real Theta = epsilon_d.trace();
epsilon_v.eye(Theta / Real(3.));
epsilon_d -= epsilon_v;
q.copy(dev_s);
q -= h;
q *= gamma_v;
q_rate.copy(dev_s);
q_rate *= gamma_v;
q_rate -= q;
q_rate /= tau;
for (UInt i = 0; i < dim; ++i) {
for (UInt j = 0; j < dim; ++j) {
*dis_energy += (epsilon_d(i, j) - alpha * q(i, j)) * q_rate(i, j) * dt;
}
}
/// Save the deviator of stress
++stress_d;
++history_int;
++dis_energy;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy() const {
AKANTU_DEBUG_IN();
Real de = 0.;
/// integrate the dissipated energy for each type of elements
for (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 <UInt dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy(
ElementType type, UInt index) const {
AKANTU_DEBUG_IN();
UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
auto it =
this->dissipated_energy(type, _not_ghost).begin(nb_quadrature_points);
UInt gindex = (this->element_filter(type, _not_ghost))(index);
AKANTU_DEBUG_OUT();
return this->fem.integrate(it[index], type, gindex);
}
/* -------------------------------------------------------------------------- */
template <UInt 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 <UInt dim>
Real MaterialStandardLinearSolidDeviatoric<dim>::getEnergy(
const std::string & energy_id, ElementType type, UInt index) {
if (energy_id == "dissipated") {
return getDissipatedEnergy(type, index);
}
if (energy_id == "dissipated_sls_deviatoric") {
return getDissipatedEnergy(type, index);
}
return MaterialElastic<dim>::getEnergy(energy_id, type, index);
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(sls_deviatoric, MaterialStandardLinearSolidDeviatoric);
} // namespace akantu

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