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weight_function_tmpl.hh
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/**
* @file weight_function_tmpl.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Apr 13 2012
* @date last modification: Thu Jun 05 2014
*
* @brief implementation of the weight function classes
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
/* Stress based weight function */
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
StressBasedWeightFunction<spatial_dimension>::StressBasedWeightFunction(Material & material) :
BaseWeightFunction<spatial_dimension>(material, "stress_based"),
stress_diag("stress_diag", material), selected_stress_diag(NULL),
stress_base("stress_base", material), selected_stress_base(NULL),
characteristic_size("lc", material), selected_characteristic_size(NULL) {
this->registerParam("ft", this->ft, 0., _pat_parsable, "Tensile strength");
stress_diag.initialize(spatial_dimension);
stress_base.initialize(spatial_dimension * spatial_dimension);
characteristic_size.initialize(1);
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void StressBasedWeightFunction<spatial_dimension>::init() {
const Mesh & mesh = this->material.getModel().getFEEngine().getMesh();
for (UInt g = _not_ghost; g <= _ghost; ++g) {
GhostType gt = GhostType(g);
Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, gt);
for(; it != last_type; ++it) {
UInt nb_quadrature_points =
this->material.getModel().getFEEngine().getNbQuadraturePoints(*it, gt);
const Array<UInt> & element_filter = this->material.getElementFilter(*it, gt);
UInt nb_element = element_filter.getSize();
Array<Real> ones(nb_element*nb_quadrature_points, 1, 1.);
Array<Real> & lc = characteristic_size(*it, gt);
this->material.getModel().getFEEngine().integrateOnQuadraturePoints(ones,
lc,
1,
*it,
gt,
element_filter);
for (UInt q = 0; q < nb_quadrature_points * nb_element; q++) {
lc(q) = pow(lc(q), 1./ Real(spatial_dimension));
}
}
}
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void StressBasedWeightFunction<spatial_dimension>::updatePrincipalStress(GhostType ghost_type) {
AKANTU_DEBUG_IN();
const Mesh & mesh = this->material.getModel().getFEEngine().getMesh();
Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
Array<Real>::const_matrix_iterator sigma =
this->material.getStress(*it, ghost_type).begin(spatial_dimension, spatial_dimension);
Array<Real>::vector_iterator eigenvalues =
stress_diag(*it, ghost_type).begin(spatial_dimension);
Array<Real>::vector_iterator eigenvalues_end =
stress_diag(*it, ghost_type).end(spatial_dimension);
Array<Real>::matrix_iterator eigenvector =
stress_base(*it, ghost_type).begin(spatial_dimension, spatial_dimension);
#ifndef __trick__
Array<Real>::iterator<Real> cl = characteristic_size(*it, ghost_type).begin();
#endif
UInt q = 0;
for(;eigenvalues != eigenvalues_end; ++sigma, ++eigenvalues, ++eigenvector, ++cl, ++q) {
sigma->eig(*eigenvalues, *eigenvector);
*eigenvalues /= ft;
#ifndef __trick__
// specify a lower bound for principal stress based on the size of the element
for (UInt i = 0; i < spatial_dimension; ++i) {
(*eigenvalues)(i) = std::max(*cl / this->R, (*eigenvalues)(i));
}
#endif
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void StressBasedWeightFunction<spatial_dimension>::selectType(ElementType type1,
GhostType ghost_type1,
ElementType type2,
GhostType ghost_type2) {
selected_stress_diag = &stress_diag(type2, ghost_type2);
selected_stress_base = &stress_base(type2, ghost_type2);
selected_characteristic_size = &characteristic_size(type1, ghost_type1);
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline Real StressBasedWeightFunction<spatial_dimension>::operator()(Real r,
const QuadraturePoint & q1,
const QuadraturePoint & q2) {
Real zero = std::numeric_limits<Real>::epsilon();
if(r < zero) return 1.; // means x and s are the same points
const Vector<Real> & x = q1.getPosition();
const Vector<Real> & s = q2.getPosition();
Vector<Real> eigs =
selected_stress_diag->begin(spatial_dimension)[q2.global_num];
Matrix<Real> eigenvects =
selected_stress_base->begin(spatial_dimension, spatial_dimension)[q2.global_num];
Real min_rho_lc = selected_characteristic_size->begin()[q1.global_num];
Vector<Real> x_s(spatial_dimension);
x_s = x;
x_s -= s;
Real rho_2 = computeRhoSquare(r, eigs, eigenvects, x_s);
Real rho_lc_2 = std::max(this->R2 * rho_2, min_rho_lc*min_rho_lc);
// Real w = std::max(0., 1. - r*r / rho_lc_2);
// w = w*w;
Real w = exp(- 2*2*r*r / rho_lc_2);
return w;
}
/* -------------------------------------------------------------------------- */
template<>
inline Real StressBasedWeightFunction<1>::computeRhoSquare(__attribute__ ((unused)) Real r,
Vector<Real> & eigs,
__attribute__ ((unused)) Matrix<Real> & eigenvects,
__attribute__ ((unused)) Vector<Real> & x_s) {
return eigs[0];
}
/* -------------------------------------------------------------------------- */
template<>
inline Real StressBasedWeightFunction<2>::computeRhoSquare(__attribute__ ((unused)) Real r,
Vector<Real> & eigs,
Matrix<Real> & eigenvects,
Vector<Real> & x_s) {
Vector<Real> u1(eigenvects.storage(), 2);
Real cos_t = x_s.dot(u1) / (x_s.norm() * u1.norm());
Real cos_t_2;
Real sin_t_2;
Real sigma1_2 = eigs[0]*eigs[0];
Real sigma2_2 = eigs[1]*eigs[1];
#ifdef __trick__
Real zero = std::numeric_limits<Real>::epsilon();
if(std::abs(cos_t) < zero) {
cos_t_2 = 0;
sin_t_2 = 1;
} else {
cos_t_2 = cos_t * cos_t;
sin_t_2 = (1 - cos_t_2);
}
Real rhop1 = std::max(0., cos_t_2 / sigma1_2);
Real rhop2 = std::max(0., sin_t_2 / sigma2_2);
#else
cos_t_2 = cos_t * cos_t;
sin_t_2 = (1 - cos_t_2);
Real rhop1 = cos_t_2 / sigma1_2;
Real rhop2 = sin_t_2 / sigma2_2;
#endif
return 1./ (rhop1 + rhop2);
}
/* -------------------------------------------------------------------------- */
template<>
inline Real StressBasedWeightFunction<3>::computeRhoSquare(Real r,
Vector<Real> & eigs,
Matrix<Real> & eigenvects,
Vector<Real> & x_s) {
Vector<Real> u1(eigenvects.storage() + 0*3, 3);
//Vector<Real> u2(eigenvects.storage() + 1*3, 3);
Vector<Real> u3(eigenvects.storage() + 2*3, 3);
Real zero = std::numeric_limits<Real>::epsilon();
Vector<Real> tmp(3);
tmp.crossProduct(x_s, u3);
Vector<Real> u3_C_x_s_C_u3(3);
u3_C_x_s_C_u3.crossProduct(u3, tmp);
Real norm_u3_C_x_s_C_u3 = u3_C_x_s_C_u3.norm();
Real cos_t = 0.;
if(std::abs(norm_u3_C_x_s_C_u3) > zero) {
Real inv_norm_u3_C_x_s_C_u3 = 1. / norm_u3_C_x_s_C_u3;
cos_t = u1.dot(u3_C_x_s_C_u3) * inv_norm_u3_C_x_s_C_u3;
}
Real cos_p = u3.dot(x_s) / r;
Real cos_t_2;
Real sin_t_2;
Real cos_p_2;
Real sin_p_2;
Real sigma1_2 = eigs[0]*eigs[0];
Real sigma2_2 = eigs[1]*eigs[1];
Real sigma3_2 = eigs[2]*eigs[2];
#ifdef __trick__
if(std::abs(cos_t) < zero) {
cos_t_2 = 0;
sin_t_2 = 1;
} else {
cos_t_2 = cos_t * cos_t;
sin_t_2 = (1 - cos_t_2);
}
if(std::abs(cos_p) < zero) {
cos_p_2 = 0;
sin_p_2 = 1;
} else {
cos_p_2 = cos_p * cos_p;
sin_p_2 = (1 - cos_p_2);
}
Real rhop1 = std::max(0., sin_p_2 * cos_t_2 / sigma1_2);
Real rhop2 = std::max(0., sin_p_2 * sin_t_2 / sigma2_2);
Real rhop3 = std::max(0., cos_p_2 / sigma3_2);
#else
cos_t_2 = cos_t * cos_t;
sin_t_2 = (1 - cos_t_2);
cos_p_2 = cos_p * cos_p;
sin_p_2 = (1 - cos_p_2);
Real rhop1 = sin_p_2 * cos_t_2 / sigma1_2;
Real rhop2 = sin_p_2 * sin_t_2 / sigma2_2;
Real rhop3 = cos_p_2 / sigma3_2;
#endif
return 1./ (rhop1 + rhop2 + rhop3);
}
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