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rAKA/src/model/solid_mechanics/material_inline_impl.cc
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/**
* @file material_inline_impl.cc
*
* @author Marco Vocialta <marco.vocialta@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
*
* @date creation: Tue Jul 27 2010
* @date last modification: Tue Sep 16 2014
*
* @brief Implementation of the inline functions of the class material
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 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/>.
*
*/
__END_AKANTU__
#include "solid_mechanics_model.hh"
#include <iostream>
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
inline UInt Material::addElement(const ElementType & type,
UInt element,
const GhostType & ghost_type) {
Array<UInt> & el_filter = element_filter(type, ghost_type);
el_filter.push_back(element);
return el_filter.getSize()-1;
}
/* -------------------------------------------------------------------------- */
inline UInt Material::getTangentStiffnessVoigtSize(UInt dim) const {
return (dim * (dim - 1) / 2 + dim);
}
/* -------------------------------------------------------------------------- */
inline UInt Material::getCauchyStressMatrixSize(UInt dim) const {
return (dim * dim);
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
inline void Material::gradUToF(const Matrix<Real> & grad_u,
Matrix<Real> & F) {
AKANTU_DEBUG_ASSERT(F.size() >= grad_u.size() && grad_u.size() == dim*dim,
"The dimension of the tensor F should be greater or equal to the dimension of the tensor grad_u.");
F.eye();
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
F(i, j) += grad_u(i, j);
}
/* -------------------------------------------------------------------------- */
template<UInt dim >
inline void Material::computeCauchyStressOnQuad(const Matrix<Real> & F,
const Matrix<Real> & piola,
Matrix<Real> & sigma,
const Real & C33 ) const {
Real J = F.det() * sqrt(C33);
Matrix<Real> F_S(dim, dim);
F_S.mul<false, false>(F, piola);
Real constant = J ? 1./J : 0;
sigma.mul<false, true>(F_S, F, constant);
}
/* -------------------------------------------------------------------------- */
inline void Material::rightCauchy(const Matrix<Real> & F,
Matrix<Real> & C) {
C.mul<true, false>(F, F);
}
/* -------------------------------------------------------------------------- */
inline void Material::leftCauchy(const Matrix<Real> & F,
Matrix<Real> & B) {
B.mul<false, true>(F, F);
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
inline void Material::gradUToEpsilon(const Matrix<Real> & grad_u,
Matrix<Real> & epsilon) {
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
epsilon(i, j) = 0.5*(grad_u(i, j) + grad_u(j, i));
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
inline void Material::gradUToGreenStrain(const Matrix<Real> & grad_u,
Matrix<Real> & epsilon) {
epsilon.mul<true, false>(grad_u, grad_u, .5);
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
epsilon(i, j) += 0.5 * (grad_u(i, j) + grad_u(j, i));
}
/* -------------------------------------------------------------------------- */
inline Real Material::stressToVonMises(const Matrix<Real> & stress) {
// compute deviatoric stress
UInt dim = stress.cols();
Matrix<Real> deviatoric_stress = Matrix<Real>::eye(dim, -1. * stress.trace() / 3.);
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
deviatoric_stress(i,j) += stress(i,j);
// return Von Mises stress
return std::sqrt(3. * deviatoric_stress.doubleDot(deviatoric_stress) / 2.);
}
/* ---------------------------------------------------------------------------*/
template<UInt dim>
inline void Material::SetCauchyStressArray(const Matrix<Real> & S_t, Matrix<Real> & Stress_vect) {
AKANTU_DEBUG_IN();
Stress_vect.clear();
//UInt cauchy_matrix_size = getCauchyStressArraySize(dim);
//see Finite ekement formulations for large deformation dynamic analysis, Bathe et al. IJNME vol 9, 1975, page 364 ^t\tau
/*
* 1d: [ s11 ]'
* 2d: [ s11 s22 s12 ]'
* 3d: [ s11 s22 s33 s23 s13 s12 ]
*/
for (UInt i = 0; i < dim; ++i)//diagonal terms
Stress_vect(i, 0) = S_t(i, i);
for (UInt i = 1; i < dim; ++i)// term s12 in 2D and terms s23 s13 in 3D
Stress_vect(dim+i-1, 0) = S_t(dim-i-1, dim-1);
for (UInt i = 2; i < dim; ++i)//term s13 in 3D
Stress_vect(dim+i, 0) = S_t(0, 1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
inline void Material::setCauchyStressMatrix(const Matrix<Real> & S_t, Matrix<Real> & Stress_matrix) {
AKANTU_DEBUG_IN();
Stress_matrix.clear();
/// see Finite ekement formulations for large deformation dynamic analysis,
/// Bathe et al. IJNME vol 9, 1975, page 364 ^t\tau
for (UInt i = 0; i < dim; ++i) {
for (UInt m = 0; m < dim; ++m) {
for (UInt n = 0; n < dim; ++n) {
Stress_matrix(i * dim + m, i * dim + n) = S_t(m, n);
}
}
}
//other terms from the diagonal
/*for (UInt i = 0; i < 3 - dim; ++i) {
Stress_matrix(dim * dim + i, dim * dim + i) = S_t(dim + i, dim + i);
}*/
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
inline Element Material::convertToLocalElement(const Element & global_element) const {
UInt ge = global_element.element;
#ifndef AKANTU_NDEBUG
UInt model_mat_index = this->model->getMaterialByElement(global_element.type,
global_element.ghost_type)(ge);
UInt mat_index = this->model->getMaterialIndex(this->name);
AKANTU_DEBUG_ASSERT(model_mat_index == mat_index,
"Conversion of a global element in a local element for the wrong material "
<< this->name << std::endl);
#endif
UInt le = this->model->getMaterialLocalNumbering(global_element.type,
global_element.ghost_type)(ge);
Element tmp_quad(global_element.type,
le,
global_element.ghost_type);
return tmp_quad;
}
/* -------------------------------------------------------------------------- */
inline Element Material::convertToGlobalElement(const Element & local_element) const {
UInt le = local_element.element;
UInt ge = this->element_filter(local_element.type, local_element.ghost_type)(le);
Element tmp_quad(local_element.type,
ge,
local_element.ghost_type);
return tmp_quad;
}
/* -------------------------------------------------------------------------- */
inline QuadraturePoint Material::convertToLocalPoint(const QuadraturePoint & global_point) const {
const FEEngine & fem = this->model->getFEEngine();
UInt nb_quad = fem.getNbQuadraturePoints(global_point.type);
Element el = this->convertToLocalElement(static_cast<const Element &>(global_point));
QuadraturePoint tmp_quad(el, global_point.num_point, nb_quad);
return tmp_quad;
}
/* -------------------------------------------------------------------------- */
inline QuadraturePoint Material::convertToGlobalPoint(const QuadraturePoint & local_point) const {
const FEEngine & fem = this->model->getFEEngine();
UInt nb_quad = fem.getNbQuadraturePoints(local_point.type);
Element el = this->convertToGlobalElement(static_cast<const Element &>(local_point));
QuadraturePoint tmp_quad(el, local_point.num_point, nb_quad);
return tmp_quad;
}
/* -------------------------------------------------------------------------- */
template<ElementType type>
inline void Material::buildElementalFieldInterpolationCoodinates(__attribute__((unused)) const Matrix<Real> & coordinates,
__attribute__((unused)) Matrix<Real> & coordMatrix) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
inline void Material::buildElementalFieldInterpolationCoodinatesLinear(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
for (UInt i = 0; i < coordinates.cols(); ++i)
coordMatrix(i, 0) = 1;
}
/* -------------------------------------------------------------------------- */
inline void Material::buildElementalFieldInterpolationCoodinatesQuadratic(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
UInt nb_quadrature_points = coordMatrix.cols();
for (UInt i = 0; i < coordinates.cols(); ++i) {
coordMatrix(i, 0) = 1;
for (UInt j = 1; j < nb_quadrature_points; ++j)
coordMatrix(i, j) = coordinates(j-1, i);
}
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_segment_2>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesLinear(coordinates, coordMatrix);
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_segment_3>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesQuadratic(coordinates, coordMatrix);
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_triangle_3>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesLinear(coordinates, coordMatrix);
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_triangle_6>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesQuadratic(coordinates, coordMatrix);
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_tetrahedron_4>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesLinear(coordinates, coordMatrix);
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_tetrahedron_10>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
buildElementalFieldInterpolationCoodinatesQuadratic(coordinates, coordMatrix);
}
/**
* @todo Write a more efficient interpolation for quadrangles by
* dropping unnecessary quadrature points
*
*/
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_quadrangle_4>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
for (UInt i = 0; i < coordinates.cols(); ++i) {
Real x = coordinates(0, i);
Real y = coordinates(1, i);
coordMatrix(i, 0) = 1;
coordMatrix(i, 1) = x;
coordMatrix(i, 2) = y;
coordMatrix(i, 3) = x * y;
}
}
/* -------------------------------------------------------------------------- */
template<>
inline void Material::buildElementalFieldInterpolationCoodinates<_quadrangle_8>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix) {
for (UInt i = 0; i < coordinates.cols(); ++i) {
UInt j = 0;
Real x = coordinates(0, i);
Real y = coordinates(1, i);
for (UInt e = 0; e <= 2; ++e) {
for (UInt n = 0; n <= 2; ++n) {
coordMatrix(i, j) = std::pow(x, e) * std::pow(y, n);
++j;
}
}
}
}
/* -------------------------------------------------------------------------- */
inline UInt Material::getNbDataForElements(const Array<Element> & elements,
SynchronizationTag tag) const {
if(tag == _gst_smm_stress) {
return (this->isFiniteDeformation() ? 3 : 1) * spatial_dimension * spatial_dimension *
sizeof(Real) * this->getModel().getNbQuadraturePoints(elements);
}
return 0;
}
/* -------------------------------------------------------------------------- */
inline void Material::packElementData(CommunicationBuffer & buffer,
const Array<Element> & elements,
SynchronizationTag tag) const {
if(tag == _gst_smm_stress) {
if(this->isFiniteDeformation()) {
packElementDataHelper(piola_kirchhoff_2, buffer, elements);
packElementDataHelper(gradu, buffer, elements);
}
packElementDataHelper(stress, buffer, elements);
}
}
/* -------------------------------------------------------------------------- */
inline void Material::unpackElementData(CommunicationBuffer & buffer,
const Array<Element> & elements,
SynchronizationTag tag) {
if(tag == _gst_smm_stress) {
if(this->isFiniteDeformation()) {
unpackElementDataHelper(piola_kirchhoff_2, buffer, elements);
unpackElementDataHelper(gradu, buffer, elements);
}
unpackElementDataHelper(stress, buffer, elements);
}
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline const T & Material::getParam(const ID & param) const {
try {
return get<T>(param);
} catch (...) {
AKANTU_EXCEPTION("No parameter " << param << " in the material " << getID());
}
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline void Material::setParam(const ID & param, T value) {
try {
set<T>(param, value);
} catch(...) {
AKANTU_EXCEPTION("No parameter " << param << " in the material " << getID());
}
updateInternalParameters();
}
/* -------------------------------------------------------------------------- */
template<typename T>
inline void Material::packElementDataHelper(const ElementTypeMapArray<T> & data_to_pack,
CommunicationBuffer & buffer,
const Array<Element> & elements,
const ID & fem_id) const {
DataAccessor::packElementalDataHelper<T>(data_to_pack, buffer, elements, true,
model->getFEEngine(fem_id));
}
/* -------------------------------------------------------------------------- */
template<typename T>
inline void Material::unpackElementDataHelper(ElementTypeMapArray<T> & data_to_unpack,
CommunicationBuffer & buffer,
const Array<Element> & elements,
const ID & fem_id) {
DataAccessor::unpackElementalDataHelper<T>(data_to_unpack, buffer, elements, true,
model->getFEEngine(fem_id));
}
/* -------------------------------------------------------------------------- */
template<> inline void Material::registerInternal<Real>(InternalField<Real> & vect) {
internal_vectors_real[vect.getID()] = &vect;
}
template<> inline void Material::registerInternal<UInt>(InternalField<UInt> & vect) {
internal_vectors_uint[vect.getID()] = &vect;
}
/* -------------------------------------------------------------------------- */
template<> inline void Material::unregisterInternal<Real>(InternalField<Real> & vect) {
internal_vectors_real.erase(vect.getID());
}
template<> inline void Material::unregisterInternal<UInt>(InternalField<UInt> & vect) {
internal_vectors_uint.erase(vect.getID());
}
/* -------------------------------------------------------------------------- */
inline bool Material::isInternal(const ID & id, const ElementKind & element_kind) const {
std::map<ID, InternalField<Real> *>::const_iterator internal_array =
internal_vectors_real.find(this->getID()+":"+id);
if (internal_array == internal_vectors_real.end()) return false;
if (internal_array->second->getElementKind() != element_kind) return false;
return true;
}
/* -------------------------------------------------------------------------- */
inline ElementTypeMap<UInt> Material::getInternalDataPerElem(const ID & id,
const ElementKind & element_kind) const {
std::map<ID, InternalField<Real> *>::const_iterator internal_array =
internal_vectors_real.find(this->getID()+":"+id);
if (internal_array == internal_vectors_real.end()) AKANTU_EXCEPTION("cannot find internal " << id);
if (internal_array->second->getElementKind() != element_kind) AKANTU_EXCEPTION("cannot find internal " << id);
InternalField<Real> & internal = *internal_array->second;
InternalField<Real>::type_iterator it = internal.firstType(spatial_dimension, _not_ghost,element_kind);
InternalField<Real>::type_iterator last_type = internal.lastType(spatial_dimension, _not_ghost,element_kind);
ElementTypeMap<UInt> res;
for(; it != last_type; ++it) {
UInt nb_quadrature_points = 0;
nb_quadrature_points = internal.getFEEngine().getNbQuadraturePoints(*it);
res(*it) = internal.getNbComponent() * nb_quadrature_points;
}
return res;
}
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