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material_iterative_stiffness_reduction.cc
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/**
* @file material_iterative_stiffness_reduction.cc
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @date Thu Feb 18 16:03:56 2016
*
* @brief Implementation of material iterative stiffness reduction
*
*
* Copyright (©) 2010-2011 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_iterative_stiffness_reduction.hh"
#include "communicator.hh"
#include "solid_mechanics_model_RVE.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
MaterialIterativeStiffnessReduction<spatial_dimension>::
MaterialIterativeStiffnessReduction(SolidMechanicsModel & model,
const ID & id)
: MaterialDamageIterative<spatial_dimension>(model, id),
eps_u("ultimate_strain", *this), D("tangent", *this), Gf(0.),
crack_band_width(0.), reduction_constant(0.) {
AKANTU_DEBUG_IN();
this->registerParam("Gf", Gf, _pat_parsable | _pat_modifiable,
"fracture energy");
this->registerParam("crack_band_width", crack_band_width,
_pat_parsable | _pat_modifiable, "crack_band_width");
this->registerParam("reduction_constant", reduction_constant, 2.,
_pat_parsable | _pat_modifiable, "reduction constant");
this->eps_u.initialize(1);
this->D.initialize(1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialIterativeStiffnessReduction<spatial_dimension>::initMaterial() {
AKANTU_DEBUG_IN();
MaterialDamageIterative<spatial_dimension>::initMaterial();
for (auto ghost_type : ghost_types) {
/// loop over all types in the filter
for (auto & el_type :
this->element_filter.elementTypes(_ghost_type = ghost_type)) {
/// get the stiffness on each quad point
auto Sc_it = this->Sc(el_type, ghost_type).begin();
/// get the tangent of the tensile softening on each quad point
auto D_it = this->D(el_type, ghost_type).begin();
auto D_end = this->D(el_type, ghost_type).end();
/// get the ultimate strain on each quad
auto eps_u_it = this->eps_u(el_type, ghost_type).begin();
// compute the tangent and the ultimate strain for each quad
for (; D_it != D_end; ++Sc_it, ++D_it, ++eps_u_it) {
*eps_u_it = ((2. * this->Gf) / (*Sc_it * this->crack_band_width));
*D_it = *(Sc_it) / ((*eps_u_it) - ((*Sc_it) / this->E));
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialIterativeStiffnessReduction<spatial_dimension>::
computeNormalizedEquivalentStress(const Array<Real> & grad_u,
ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
/// storage for the current stress
Matrix<Real> sigma(spatial_dimension, spatial_dimension);
/// Vector to store eigenvalues of current stress tensor
Vector<Real> eigenvalues(spatial_dimension);
/// iterators on the needed internal fields
auto Sc_it = this->Sc(el_type, ghost_type).begin();
auto dam_it = this->damage(el_type, ghost_type).begin();
auto equivalent_stress_it =
this->equivalent_stress(el_type, ghost_type).begin();
auto grad_u_it = grad_u.begin(spatial_dimension, spatial_dimension);
auto grad_u_end = grad_u.end(spatial_dimension, spatial_dimension);
/// loop over all the quadrature points and compute the equivalent stress
for (; grad_u_it != grad_u_end; ++grad_u_it) {
/// compute the stress
sigma.zero();
MaterialElastic<spatial_dimension>::computeStressOnQuad(*grad_u_it, sigma,
0.);
MaterialDamageIterative<spatial_dimension>::computeDamageAndStressOnQuad(
sigma, *dam_it);
/// compute eigenvalues
sigma.eig(eigenvalues);
/// find max eigenvalue and normalize by tensile strength
*equivalent_stress_it =
*(std::max_element(eigenvalues.storage(),
eigenvalues.storage() + spatial_dimension)) /
(*Sc_it);
++Sc_it;
++equivalent_stress_it;
++dam_it;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
UInt MaterialIterativeStiffnessReduction<spatial_dimension>::updateDamage() {
UInt nb_damaged_elements = 0;
if (this->norm_max_equivalent_stress >= 1.) {
AKANTU_DEBUG_IN();
/// update the damage only on non-ghosts elements! Doesn't make sense to
/// update on ghost.
GhostType ghost_type = _not_ghost;
/// loop over all the elements
for (auto && el_type : this->model.getFEEngine().getMesh().elementTypes(
spatial_dimension, ghost_type)) {
/// get iterators on the needed internal fields
auto equivalent_stress_it =
this->equivalent_stress(el_type, ghost_type).begin();
auto equivalent_stress_end =
this->equivalent_stress(el_type, ghost_type).end();
auto dam_it = this->damage(el_type, ghost_type).begin();
auto reduction_it = this->reduction_step(el_type, ghost_type).begin();
auto eps_u_it = this->eps_u(el_type, ghost_type).begin();
auto Sc_it = this->Sc(el_type, ghost_type).begin();
auto D_it = this->D(el_type, ghost_type).begin();
/// loop over all the quads of the given element type
for (; equivalent_stress_it != equivalent_stress_end;
++equivalent_stress_it, ++dam_it, ++reduction_it, ++eps_u_it,
++Sc_it, ++D_it) {
/// check if damage occurs
if (*equivalent_stress_it >=
(1 - this->dam_tolerance) * this->norm_max_equivalent_stress) {
/// check if this element can still be damaged
if (*reduction_it == this->max_reductions)
continue;
/// increment the counter of stiffness reduction steps
*reduction_it += 1;
if (*reduction_it == this->max_reductions)
*dam_it = this->max_damage;
else {
/// update the damage on this quad
*dam_it =
1. - (1. / std::pow(this->reduction_constant, *reduction_it));
/// update the stiffness on this quad
*Sc_it = (*eps_u_it) * (1. - (*dam_it)) * this->E * (*D_it) /
((1. - (*dam_it)) * this->E + (*D_it));
}
nb_damaged_elements += 1;
}
}
}
}
auto rve_model = dynamic_cast<SolidMechanicsModelRVE *>(&this->model);
if (rve_model == NULL) {
const auto & comm = this->model.getMesh().getCommunicator();
comm.allReduce(nb_damaged_elements, SynchronizerOperation::_sum);
}
AKANTU_DEBUG_OUT();
return nb_damaged_elements;
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(iterative_stiffness_reduction,
MaterialIterativeStiffnessReduction);
} // namespace akantu

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