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material_cohesive.cc
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/**
* @file material_cohesive.cc
*
* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Feb 22 2012
* @date last modification: Tue Jul 29 2014
*
* @brief Specialization of the material class for cohesive elements
*
* @section LICENSE
*
* Copyright (©) 2014 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_cohesive.hh"
#include "solid_mechanics_model_cohesive.hh"
#include "sparse_matrix.hh"
#include "dof_synchronizer.hh"
#include "aka_random_generator.hh"
#include "shape_cohesive.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
MaterialCohesive::MaterialCohesive(SolidMechanicsModel & model, const ID & id) :
Material(model, id),
facet_filter("facet_filter", id, this->getMemoryID()),
fem_cohesive(&(model.getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine"))),
reversible_energy("reversible_energy", *this),
total_energy("total_energy", *this),
opening("opening", *this),
opening_old("opening (old)", *this),
tractions("tractions", *this),
tractions_old("tractions (old)", *this),
contact_tractions("contact_tractions", *this),
contact_opening("contact_opening", *this),
delta_max("delta max", *this),
use_previous_delta_max(false),
damage("damage", *this),
sigma_c("sigma_c", *this) {
AKANTU_DEBUG_IN();
this->model = dynamic_cast<SolidMechanicsModelCohesive*>(&model);
this->registerParam("sigma_c", sigma_c,
_pat_parsable | _pat_readable, "Critical stress");
this->registerParam("delta_c", delta_c, 0.,
_pat_parsable | _pat_readable, "Critical displacement");
this->model->getMesh().initElementTypeMapArray(this->element_filter,
1,
spatial_dimension,
false,
_ek_cohesive);
if (this->model->getIsExtrinsic())
this->model->getMeshFacets().initElementTypeMapArray(facet_filter, 1,
spatial_dimension - 1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
MaterialCohesive::~MaterialCohesive() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::initMaterial() {
AKANTU_DEBUG_IN();
Material::initMaterial();
this->reversible_energy.initialize(1 );
this->total_energy .initialize(1 );
this->tractions_old .initialize(spatial_dimension);
this->tractions .initialize(spatial_dimension);
this->opening_old .initialize(spatial_dimension);
this->contact_tractions.initialize(spatial_dimension);
this->contact_opening .initialize(spatial_dimension);
this->opening .initialize(spatial_dimension);
this->delta_max .initialize(1 );
this->damage .initialize(1 );
if (model->getIsExtrinsic()) this->sigma_c.initialize(1);
if (use_previous_delta_max) delta_max.initializeHistory();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::assembleResidual(GhostType ghost_type) {
AKANTU_DEBUG_IN();
#if defined(AKANTU_DEBUG_TOOLS)
debug::element_manager.printData(debug::_dm_material_cohesive,
"Cohesive Tractions",
tractions);
#endif
Array<Real> & residual = const_cast<Array<Real> &>(model->getResidual());
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
ghost_type, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
ghost_type, _ek_cohesive);
for(; it != last_type; ++it) {
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
UInt nb_element = elem_filter.getSize();
if (nb_element == 0) continue;
const Array<Real> & shapes = fem_cohesive->getShapes(*it, ghost_type);
Array<Real> & traction = tractions(*it, ghost_type);
Array<Real> & contact_traction = contact_tractions(*it, ghost_type);
UInt size_of_shapes = shapes.getNbComponent();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
UInt nb_quadrature_points = fem_cohesive->getNbQuadraturePoints(*it, ghost_type);
/// compute @f$t_i N_a@f$
Array<Real> * traction_cpy = new Array<Real>(nb_element * nb_quadrature_points,
spatial_dimension * size_of_shapes);
Array<Real>::iterator<Matrix<Real> > traction_it
= traction.begin(spatial_dimension, 1);
Array<Real>::iterator<Matrix<Real> > contact_traction_it
= contact_traction.begin(spatial_dimension, 1);
Array<Real>::const_iterator<Matrix<Real> > shapes_filtered_begin
= shapes.begin(1, size_of_shapes);
Array<Real>::iterator<Matrix<Real> > traction_cpy_it
= traction_cpy->begin(spatial_dimension, size_of_shapes);
Matrix<Real> traction_tmp(spatial_dimension, 1);
for (UInt el = 0; el < nb_element; ++el) {
UInt current_quad = elem_filter(el) * nb_quadrature_points;
for (UInt q = 0; q < nb_quadrature_points; ++q, ++traction_it,
++contact_traction_it, ++current_quad, ++traction_cpy_it) {
const Matrix<Real> & shapes_filtered = shapes_filtered_begin[current_quad];
traction_tmp.copy(*traction_it);
traction_tmp += *contact_traction_it;
traction_cpy_it->mul<false, false>(traction_tmp, shapes_filtered);
}
}
/**
* compute @f$\int t \cdot N\, dS@f$ by @f$ \sum_q \mathbf{N}^t
* \mathbf{t}_q \overline w_q J_q@f$
*/
Array<Real> * int_t_N = new Array<Real>(nb_element,
spatial_dimension*size_of_shapes,
"int_t_N");
fem_cohesive->integrate(*traction_cpy, *int_t_N,
spatial_dimension * size_of_shapes,
*it, ghost_type,
elem_filter);
delete traction_cpy;
int_t_N->extendComponentsInterlaced(2, int_t_N->getNbComponent());
Real * int_t_N_val = int_t_N->storage();
for (UInt el = 0; el < nb_element; ++el) {
for (UInt n = 0; n < size_of_shapes * spatial_dimension; ++n)
int_t_N_val[n] *= -1.;
int_t_N_val += nb_nodes_per_element * spatial_dimension;
}
/// assemble
model->getFEEngineBoundary().assembleArray(*int_t_N, residual,
model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
residual.getNbComponent(),
*it, ghost_type, elem_filter, 1);
delete int_t_N;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::assembleStiffnessMatrix(GhostType ghost_type) {
AKANTU_DEBUG_IN();
SparseMatrix & K = const_cast<SparseMatrix &>(model->getStiffnessMatrix());
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
ghost_type, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
ghost_type, _ek_cohesive);
for(; it != last_type; ++it) {
UInt nb_quadrature_points = fem_cohesive->getNbQuadraturePoints(*it, ghost_type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
const Array<Real> & shapes = fem_cohesive->getShapes(*it, ghost_type);
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
UInt nb_element = elem_filter.getSize();
if(!nb_element) continue;
UInt size_of_shapes = shapes.getNbComponent();
Array<Real> * shapes_filtered =
new Array<Real>(nb_element*nb_quadrature_points,
size_of_shapes, "filtered shapes");
Real * shapes_val = shapes.storage();
Real * shapes_filtered_val = shapes_filtered->storage();
UInt * elem_filter_val = elem_filter.storage();
for (UInt el = 0; el < nb_element; ++el) {
shapes_val = shapes.storage() + elem_filter_val[el] *
size_of_shapes * nb_quadrature_points;
memcpy(shapes_filtered_val, shapes_val,
size_of_shapes * nb_quadrature_points * sizeof(Real));
shapes_filtered_val += size_of_shapes * nb_quadrature_points;
}
/**
* compute A matrix @f$ \mathbf{A} = \left[\begin{array}{c c c c c c c c c c c c}
* 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\
* 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\
* 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\
* 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\
* 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 \\
* 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1
* \end{array} \right]@f$
**/
// UInt size_of_A = spatial_dimension*size_of_shapes*spatial_dimension*nb_nodes_per_element;
// Real * A = new Real[size_of_A];
// memset(A, 0, size_of_A*sizeof(Real));
Matrix<Real> A(spatial_dimension*size_of_shapes,
spatial_dimension*nb_nodes_per_element);
for ( UInt i = 0; i < spatial_dimension*size_of_shapes; ++i) {
A(i, i) = 1;
A(i, i + spatial_dimension*size_of_shapes) = -1;
}
/// compute traction
computeTraction(ghost_type);
/// get the tangent matrix @f$\frac{\partial{(t/\delta)}}{\partial{\delta}} @f$
Array<Real> * tangent_stiffness_matrix =
new Array<Real>(nb_element * nb_quadrature_points,
spatial_dimension * spatial_dimension,
"tangent_stiffness_matrix");
// Array<Real> * normal = new Array<Real>(nb_element * nb_quadrature_points, spatial_dimension, "normal");
Array<Real> normal(nb_quadrature_points, spatial_dimension, "normal");
computeNormal(model->getCurrentPosition(), normal, *it, ghost_type);
tangent_stiffness_matrix->clear();
computeTangentTraction(*it, *tangent_stiffness_matrix, normal, ghost_type);
// delete normal;
UInt size_at_nt_d_n_a = spatial_dimension*nb_nodes_per_element*spatial_dimension*nb_nodes_per_element;
Array<Real> * at_nt_d_n_a = new Array<Real> (nb_element*nb_quadrature_points,
size_at_nt_d_n_a,
"A^t*N^t*D*N*A");
Array<Real>::iterator<Vector<Real> > shapes_filt_it =
shapes_filtered->begin(size_of_shapes);
Array<Real>::matrix_iterator D_it =
tangent_stiffness_matrix->begin(spatial_dimension, spatial_dimension);
Array<Real>::matrix_iterator At_Nt_D_N_A_it =
at_nt_d_n_a->begin(spatial_dimension * nb_nodes_per_element,
spatial_dimension * nb_nodes_per_element);
Array<Real>::matrix_iterator At_Nt_D_N_A_end =
at_nt_d_n_a->end(spatial_dimension * nb_nodes_per_element,
spatial_dimension * nb_nodes_per_element);
Matrix<Real> N (spatial_dimension, spatial_dimension * size_of_shapes);
Matrix<Real> N_A (spatial_dimension, spatial_dimension * nb_nodes_per_element);
Matrix<Real> D_N_A(spatial_dimension, spatial_dimension * nb_nodes_per_element);
for(; At_Nt_D_N_A_it != At_Nt_D_N_A_end; ++At_Nt_D_N_A_it, ++D_it, ++shapes_filt_it) {
N.clear();
/**
* store the shapes in voigt notations matrix @f$\mathbf{N} =
* \begin{array}{cccccc} N_0(\xi) & 0 & N_1(\xi) &0 & N_2(\xi) & 0 \\
* 0 & * N_0(\xi)& 0 &N_1(\xi)& 0 & N_2(\xi) \end{array} @f$
**/
for (UInt i = 0; i < spatial_dimension ; ++i)
for (UInt n = 0; n < size_of_shapes; ++n)
N(i, i + spatial_dimension * n) = (*shapes_filt_it)(n);
/**
* compute stiffness matrix @f$ \mathbf{K} = \delta \mathbf{U}^T
* \int_{\Gamma_c} {\mathbf{P}^t \frac{\partial{\mathbf{t}}} {\partial{\delta}}
* \mathbf{P} d\Gamma \Delta \mathbf{U}} @f$
**/
N_A.mul<false, false>(N, A);
D_N_A.mul<false, false>(*D_it, N_A);
(*At_Nt_D_N_A_it).mul<true, false>(D_N_A, N_A);
}
delete tangent_stiffness_matrix;
delete shapes_filtered;
Array<Real> * K_e = new Array<Real>(nb_element, size_at_nt_d_n_a,
"K_e");
fem_cohesive->integrate(*at_nt_d_n_a, *K_e,
size_at_nt_d_n_a,
*it, ghost_type,
elem_filter);
delete at_nt_d_n_a;
model->getFEEngine().assembleMatrix(*K_e, K, spatial_dimension,
*it, ghost_type, elem_filter);
delete K_e;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- *
* Compute traction from displacements
*
* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
*/
void MaterialCohesive::computeTraction(GhostType ghost_type) {
AKANTU_DEBUG_IN();
#if defined(AKANTU_DEBUG_TOOLS)
debug::element_manager.printData(debug::_dm_material_cohesive,
"Cohesive Openings",
opening);
#endif
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
ghost_type, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
ghost_type, _ek_cohesive);
for(; it != last_type; ++it) {
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
UInt nb_element = elem_filter.getSize();
if (nb_element == 0) continue;
UInt nb_quadrature_points =
nb_element*fem_cohesive->getNbQuadraturePoints(*it, ghost_type);
Array<Real> normal(nb_quadrature_points, spatial_dimension, "normal");
/// compute normals @f$\mathbf{n}@f$
computeNormal(model->getCurrentPosition(), normal, *it, ghost_type);
/// compute openings @f$\mathbf{\delta}@f$
computeOpening(model->getDisplacement(), opening(*it, ghost_type), *it, ghost_type);
/// compute traction @f$\mathbf{t}@f$
computeTraction(normal, *it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::computeNormal(const Array<Real> & position,
Array<Real> & normal,
ElementType type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
if (type == _cohesive_1d_2)
fem_cohesive->computeNormalsOnControlPoints(position,
normal,
type, ghost_type);
else {
#define COMPUTE_NORMAL(type) \
fem_cohesive->getShapeFunctions(). \
computeNormalsOnControlPoints<type, CohesiveReduceFunctionMean>(position, \
normal, \
ghost_type, \
element_filter(type, ghost_type));
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_NORMAL);
#undef COMPUTE_NORMAL
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::computeOpening(const Array<Real> & displacement,
Array<Real> & opening,
ElementType type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
#define COMPUTE_OPENING(type) \
fem_cohesive->getShapeFunctions(). \
interpolateOnControlPoints<type, CohesiveReduceFunctionOpening>(displacement, \
opening, \
spatial_dimension, \
ghost_type, \
element_filter(type, ghost_type));
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_OPENING);
#undef COMPUTE_OPENING
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void MaterialCohesive::computeEnergies() {
AKANTU_DEBUG_IN();
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it =
mesh.firstType(spatial_dimension, _not_ghost, _ek_cohesive);
Mesh::type_iterator last_type =
mesh.lastType(spatial_dimension, _not_ghost, _ek_cohesive);
Real * memory_space = new Real[2*spatial_dimension];
Vector<Real> b(memory_space, spatial_dimension);
Vector<Real> h(memory_space + spatial_dimension, spatial_dimension);
for(; it != last_type; ++it) {
Array<Real>::iterator<Real> erev =
reversible_energy(*it, _not_ghost).begin();
Array<Real>::iterator<Real> etot =
total_energy(*it, _not_ghost).begin();
Array<Real>::vector_iterator traction_it =
tractions(*it, _not_ghost).begin(spatial_dimension);
Array<Real>::vector_iterator traction_old_it =
tractions_old(*it, _not_ghost).begin(spatial_dimension);
Array<Real>::vector_iterator opening_it =
opening(*it, _not_ghost).begin(spatial_dimension);
Array<Real>::vector_iterator opening_old_it =
opening_old(*it, _not_ghost).begin(spatial_dimension);
Array<Real>::vector_iterator traction_end =
tractions(*it, _not_ghost).end(spatial_dimension);
/// loop on each quadrature point
for (; traction_it != traction_end;
++traction_it, ++traction_old_it,
++opening_it, ++opening_old_it,
++erev, ++etot) {
/// trapezoidal integration
b = *opening_it;
b -= *opening_old_it;
h = *traction_old_it;
h += *traction_it;
*etot += .5 * b.dot(h);
*erev = .5 * traction_it->dot(*opening_it);
}
}
delete [] memory_space;
/// update old values
it = mesh.firstType(spatial_dimension, _not_ghost, _ek_cohesive);
GhostType ghost_type = _not_ghost;
for(; it != last_type; ++it) {
tractions_old(*it, ghost_type).copy(tractions(*it, ghost_type));
opening_old(*it, ghost_type).copy(opening(*it, ghost_type));
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Real MaterialCohesive::getReversibleEnergy() {
AKANTU_DEBUG_IN();
Real erev = 0.;
/// integrate reversible energy for each type of elements
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
_not_ghost, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
_not_ghost, _ek_cohesive);
for(; it != last_type; ++it) {
erev += fem_cohesive->integrate(reversible_energy(*it, _not_ghost), *it,
_not_ghost, element_filter(*it, _not_ghost));
}
AKANTU_DEBUG_OUT();
return erev;
}
/* -------------------------------------------------------------------------- */
Real MaterialCohesive::getDissipatedEnergy() {
AKANTU_DEBUG_IN();
Real edis = 0.;
/// integrate dissipated energy for each type of elements
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
_not_ghost, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
_not_ghost, _ek_cohesive);
for(; it != last_type; ++it) {
Array<Real> dissipated_energy(total_energy(*it, _not_ghost));
dissipated_energy -= reversible_energy(*it, _not_ghost);
edis += fem_cohesive->integrate(dissipated_energy, *it,
_not_ghost, element_filter(*it, _not_ghost));
}
AKANTU_DEBUG_OUT();
return edis;
}
/* -------------------------------------------------------------------------- */
Real MaterialCohesive::getContactEnergy() {
AKANTU_DEBUG_IN();
Real econ = 0.;
/// integrate contact energy for each type of elements
Mesh & mesh = fem_cohesive->getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension,
_not_ghost, _ek_cohesive);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
_not_ghost, _ek_cohesive);
for(; it != last_type; ++it) {
Array<UInt> & el_filter = element_filter(*it, _not_ghost);
UInt nb_quad_per_el = fem_cohesive->getNbQuadraturePoints(*it, _not_ghost);
UInt nb_quad_points = el_filter.getSize() * nb_quad_per_el;
Array<Real> contact_energy(nb_quad_points);
Array<Real>::vector_iterator contact_traction_it =
contact_tractions(*it, _not_ghost).begin(spatial_dimension);
Array<Real>::vector_iterator contact_opening_it =
contact_opening(*it, _not_ghost).begin(spatial_dimension);
/// loop on each quadrature point
for (UInt el = 0; el < nb_quad_points;
++contact_traction_it, ++contact_opening_it, ++el) {
contact_energy(el) = .5 * contact_traction_it->dot(*contact_opening_it);
}
econ += fem_cohesive->integrate(contact_energy, *it,
_not_ghost, el_filter);
}
AKANTU_DEBUG_OUT();
return econ;
}
/* -------------------------------------------------------------------------- */
Real MaterialCohesive::getEnergy(std::string type) {
AKANTU_DEBUG_IN();
if (type == "reversible") return getReversibleEnergy();
else if (type == "dissipated") return getDissipatedEnergy();
else if (type == "cohesive contact") return getContactEnergy();
AKANTU_DEBUG_OUT();
return 0.;
}
/* -------------------------------------------------------------------------- */
__END_AKANTU__
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