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material_iterative_stiffness_reduction.cc
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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
*
* @section LICENSE
*
* 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 "solid_mechanics_model_RVE.hh"
#include <math.h>
namespace akantu {
template<UInt spatial_dimension>
/* -------------------------------------------------------------------------- */
MaterialIterativeStiffnessReduction<spatial_dimension>::MaterialIterativeStiffnessReduction(SolidMechanicsModel & model,
const ID & id) :
Material(model, 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 (ghost_type_t::iterator g = ghost_type_t::begin(); g != ghost_type_t::end(); ++g) {
GhostType ghost_type = *g;
/// loop over all types in the material
typedef ElementTypeMapArray<UInt>:: type_iterator iterator;
iterator it = this->element_filter.firstType(spatial_dimension, ghost_type, _ek_regular);
iterator last_type = this->element_filter.lastType(spatial_dimension, ghost_type, _ek_regular);
/// loop over all types in the filter
for(; it != last_type; ++it) {
ElementType el_type = *it;
/// get the stiffness on each quad point
Array<Real>::const_iterator<Real> Sc_it = this->Sc(el_type, ghost_type).begin();
/// get the tangent of the tensile softening on each quad point
Array<Real>::iterator<Real> D_it = this->D(el_type, ghost_type).begin();
Array<Real>::iterator<Real> D_end = this->D(el_type, ghost_type).end();
/// get the ultimate strain on each quad
Array<Real>::iterator<Real> 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
Array<Real>::const_scalar_iterator Sc_it = this->Sc(el_type, ghost_type).begin();
Array<Real>::scalar_iterator dam_it = this->damage(el_type, ghost_type).begin();
Array<Real>::scalar_iterator equivalent_stress_it = this->equivalent_stress(el_type, ghost_type).begin();
Array<Real>::const_matrix_iterator grad_u_it = grad_u.begin(spatial_dimension,
spatial_dimension);
Array<Real>::const_matrix_iterator 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.clear();
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;;
Mesh::type_iterator it = this->model.getFEEngine().getMesh().firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = this->model.getFEEngine().getMesh().lastType(spatial_dimension, ghost_type);
/// loop over all the elements
for(; it != last_type; ++it) {
ElementType el_type = *it;
/// get iterators on the needed internal fields
Array<Real>::const_scalar_iterator equivalent_stress_it = this->equivalent_stress(el_type, ghost_type).begin();
Array<Real>::const_scalar_iterator equivalent_stress_end = this->equivalent_stress(el_type, ghost_type).end();
Array<Real>::scalar_iterator dam_it = this->damage(el_type, ghost_type).begin();
Array<UInt>::scalar_iterator reduction_it = this->reduction_step(el_type, ghost_type).begin();
Array<Real>::const_scalar_iterator eps_u_it = this->eps_u(el_type, ghost_type).begin();
Array<Real>::scalar_iterator Sc_it = this->Sc(el_type, ghost_type).begin();
Array<Real>::const_scalar_iterator 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;
}
}
}
}
const SolidMechanicsModelRVE * rve_model = dynamic_cast<const SolidMechanicsModelRVE *>(this->model);
if (rve_model == NULL) {
StaticCommunicator & comm = akantu::StaticCommunicator::getStaticCommunicator();
comm.allReduce(&nb_damaged_elements, 1, _so_sum);
}
AKANTU_DEBUG_OUT();
return nb_damaged_elements;
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(MaterialIterativeStiffnessReduction);
} // namespace akantu

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