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resolution.cc
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/**
* @file resolution.cc
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Mon Jan 7 2019
* @date last modification: Mon Jan 7 2019
*
* @brief Implementation of common part of the contact resolution class
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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 "resolution.hh"
#include "contact_mechanics_model.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
Resolution::Resolution(ContactMechanicsModel & model, const ID & id)
: Memory(id, model.getMemoryID()), Parsable(ParserType::_contact_resolution, id),
fem(model.getFEEngine()),
name(""), model(model),
spatial_dimension(model.getMesh().getSpatialDimension()){
AKANTU_DEBUG_IN();
this->initialize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Resolution::~Resolution() = default;
/* -------------------------------------------------------------------------- */
void Resolution::initialize() {
registerParam("name", name, std::string(), _pat_parsable | _pat_readable);
registerParam("mu", mu, Real(0.), _pat_parsable | _pat_modifiable,
"Friciton Coefficient");
}
/* -------------------------------------------------------------------------- */
void Resolution::printself(std::ostream & stream, int indent) const {
std::string space;
for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
;
std::string type = getID().substr(getID().find_last_of(':') + 1);
stream << space << "Contact Resolution " << type << " [" << std::endl;
Parsable::printself(stream, indent);
stream << space << "]" << std::endl;
}
/* -------------------------------------------------------------------------- */
void Resolution::assembleInternalForces(GhostType ghost_type) {
AKANTU_DEBUG_IN();
auto & internal_force =
const_cast<Array<Real> &>(model.getInternalForce());
auto & contact_area =
const_cast<Array<Real> &>(model.getContactArea());
auto & contact_map = model.getContactMap();
const auto slave_nodes = model.getMesh().getElementGroup(name).getNodes();
for (auto & slave: slave_nodes) {
if (contact_map.find(slave) == contact_map.end())
continue;
auto & master = contact_map[slave].master;
auto & gap = contact_map[slave].gap;
auto & projection = contact_map[slave].projection;
auto & normal = contact_map[slave].normal;
const auto & connectivity = contact_map[slave].connectivity;
const ElementType & type = master.type;
UInt nb_nodes_master = Mesh::getNbNodesPerElement(master.type);
Vector<Real> shapes(nb_nodes_master);
Matrix<Real> shapes_derivatives(spatial_dimension - 1, nb_nodes_master);
#define GET_SHAPES_NATURAL(type) \
ElementClass<type>::computeShapes(projection, shapes)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPES_NATURAL);
#undef GET_SHAPES_NATURAL
#define GET_SHAPE_DERIVATIVES_NATURAL(type) \
ElementClass<type>::computeDNDS(projection, shapes_derivatives)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_DERIVATIVES_NATURAL);
#undef GET_SHAPE_DERIVATIVES_NATURAL
Vector<Real> elem_force(connectivity.size() * spatial_dimension);
Matrix<Real> tangents(spatial_dimension - 1, spatial_dimension);
Matrix<Real> global_coords(nb_nodes_master, spatial_dimension);
computeCoordinates(master, global_coords);
computeTangents(shapes_derivatives, global_coords, tangents);
Matrix<Real> surface_matrix(spatial_dimension - 1, spatial_dimension - 1);
computeSurfaceMatrix(tangents, surface_matrix);
Vector<Real> n(connectivity.size() * spatial_dimension);
computeN(n, shapes, normal);
computeNormalForce(elem_force, n, gap);
Array<Real> t_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
Array<Real> n_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
Array<Real> d_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
computeTalpha(t_alpha, shapes, tangents);
computeNalpha(n_alpha, shapes_derivatives, normal);
computeDalpha(d_alpha, n_alpha, t_alpha, surface_matrix, gap);
//computeFrictionForce(elem_force, d_alpha, gap);
UInt nb_degree_of_freedom = internal_force.getNbComponent();
for (UInt i = 0; i < connectivity.size(); ++i) {
UInt n = connectivity[i];
for (UInt j = 0; j < nb_degree_of_freedom; ++j) {
UInt offset_node = n * nb_degree_of_freedom + j;
internal_force[offset_node] += elem_force[i*nb_degree_of_freedom + j];
internal_force[offset_node] *= contact_area[n];
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Resolution::assembleStiffnessMatrix(GhostType ghost_type) {
AKANTU_DEBUG_IN();
auto & contact_stiffness =
const_cast<SparseMatrix &>(model.getDOFManager().getMatrix("K"));
const auto slave_nodes =
model.getMesh().getElementGroup(name).getNodes();
auto & contact_map = model.getContactMap();
for (auto & slave: slave_nodes) {
if (contact_map.find(slave) == contact_map.end()) {
continue;
}
auto & master = contact_map[slave].master;
auto & gap = contact_map[slave].gap;
auto & projection = contact_map[slave].projection;
auto & normal = contact_map[slave].normal;
const auto & connectivity = contact_map[slave].connectivity;
const ElementType & type = master.type;
UInt nb_nodes_master = Mesh::getNbNodesPerElement(master.type);
Vector<Real> shapes(nb_nodes_master);
Matrix<Real> shapes_derivatives(spatial_dimension - 1, nb_nodes_master);
#define GET_SHAPES_NATURAL(type) \
ElementClass<type>::computeShapes(projection, shapes)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPES_NATURAL);
#undef GET_SHAPES_NATURAL
#define GET_SHAPE_DERIVATIVES_NATURAL(type) \
ElementClass<type>::computeDNDS(projection, shapes_derivatives)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_DERIVATIVES_NATURAL);
#undef GET_SHAPE_DERIVATIVES_NATURAL
Matrix<Real> elementary_stiffness(connectivity.size() * spatial_dimension,
connectivity.size() * spatial_dimension);
Matrix<Real> tangents(spatial_dimension - 1, spatial_dimension);
Matrix<Real> global_coords(nb_nodes_master, spatial_dimension);
computeCoordinates(master, global_coords);
computeTangents(shapes_derivatives, global_coords, tangents);
Matrix<Real> surface_matrix(spatial_dimension - 1, spatial_dimension - 1);
computeSurfaceMatrix(tangents, surface_matrix);
Vector<Real> n(connectivity.size() * spatial_dimension);
Array<Real> t_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
Array<Real> n_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
Array<Real> d_alpha(connectivity.size() * spatial_dimension, spatial_dimension - 1);
computeN( n, shapes, normal);
computeTalpha( t_alpha, shapes, tangents);
computeNalpha( n_alpha, shapes_derivatives, normal);
computeDalpha( d_alpha, n_alpha, t_alpha, surface_matrix, gap);
Matrix<Real> kc(connectivity.size() * spatial_dimension,
connectivity.size() * spatial_dimension);
computeTangentModuli(kc, n, n_alpha, d_alpha, surface_matrix, gap);
std::vector<UInt> equations;
UInt nb_degree_of_freedom = model.getSpatialDimension();
for (UInt i : arange(connectivity.size())) {
UInt n = connectivity[i];
for (UInt j : arange(nb_degree_of_freedom))
equations.push_back(n * nb_degree_of_freedom + j);
}
for (UInt i : arange(kc.rows())) {
UInt row = equations[i];
for (UInt j : arange(kc.cols())) {
UInt col = equations[j];
contact_stiffness.add(row, col, kc(i, j));
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Resolution::computeTangents(Matrix<Real> & shapes_derivatives, Matrix<Real> & global_coords,
Matrix<Real> & tangents) {
/*UInt index = 0;
for (auto && values : zip(make_view(tangents, spatial_dimension))) {
auto & tangent = std::get<0>(values);
for (UInt n : arange(global_coords.getNbComponent())) {
tangent += shapes_derivatives(n, index) * global_coords(n);
}
++index;
}*/
tangents.mul<false, true>(shapes_derivatives, global_coords);
}
/* -------------------------------------------------------------------------- */
void Resolution::computeSurfaceMatrix(Matrix<Real> & tangents, Matrix<Real> & surface_matrix) {
/*Matrix<Real> A(surface_matrix);
for (UInt i : arange(spatial_dimension - 1)) {
for (UInt j : arange(spatial_dimension -1 )) {
A(i, j) = tangents(i) * tangents(j);
}
}*/
surface_matrix.mul<false, true>(tangents, tangents);
surface_matrix = surface_matrix.inverse();
//A.inverse(surface_matrix);
}
/* -------------------------------------------------------------------------- */
void Resolution::computeN(Vector<Real> & n, Vector<Real> & shapes, Vector<Real> & normal) {
UInt dim = normal.size();
for (UInt i = 0; i < dim; ++i) {
n[i] = normal[i];
for (UInt j = 0; j < shapes.size(); ++j) {
n[(1 + j) * dim + i] = -normal[i] * shapes[j];
}
}
}
/* -------------------------------------------------------------------------- */
void Resolution::computeTalpha(Array<Real> & t_alpha, Vector<Real> & shapes,
Matrix<Real> & tangents) {
for (auto && values:
zip(tangents.transpose(),
make_view(t_alpha, t_alpha.size()))) {
auto & tangent = std::get<0>(values);
auto & t_s = std::get<1>(values);
for (UInt i : arange(spatial_dimension)) {
t_s[i] = -tangent(i);
for (UInt j : arange(shapes.size())) {
t_s[(1 + j)*spatial_dimension + i] = -shapes[j] * tangent(i);
}
}
}
}
/* -------------------------------------------------------------------------- */
void Resolution::computeNalpha(Array<Real> & n_alpha, Matrix<Real> & shapes_derivatives,
Vector<Real> & normal) {
for (auto && values:
zip(shapes_derivatives.transpose(),
make_view(n_alpha, n_alpha.size()))) {
auto & dnds = std::get<0>(values);
auto & n_s = std::get<1>(values);
for (UInt i : arange(spatial_dimension)) {
n_s[i] = 0;
for (UInt j : arange(shapes_derivatives.size())) {
n_s[(1 + j)*spatial_dimension + i] = -shapes_derivatives[j]*normal[i];
}
}
}
}
/* -------------------------------------------------------------------------- */
void Resolution::computeDalpha(Array<Real> & d_alpha, Array<Real> & n_alpha,
Array<Real> & t_alpha, Matrix<Real> & surface_matrix,
Real & gap) {
for (auto && entry : zip(surface_matrix.transpose(),
make_view(d_alpha, d_alpha.size()))) {
auto & a_s = std::get<0>(entry);
auto & d_s = std::get<1>(entry);
for (auto && values :
zip(arange(t_alpha.size()),
make_view(t_alpha, t_alpha.size()),
make_view(n_alpha, n_alpha.size()))) {
auto & index = std::get<0>(values);
auto & t_s = std::get<1>(values);
auto & n_s = std::get<2>(values);
d_s += (t_s + gap * n_s);
d_s *= a_s(index);
}
}
}
/* -------------------------------------------------------------------------- */
void Resolution::computeCoordinates(const Element & el, Matrix<Real> & coords) {
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(el.type);
Vector<UInt> connect = model.getMesh().getConnectivity(el.type, _not_ghost)
.begin(nb_nodes_per_element)[el.element];
// change this to current position
auto & positions = model.getMesh().getNodes();
for (UInt n = 0; n < nb_nodes_per_element; ++n) {
UInt node = connect[n];
for (UInt s: arange(spatial_dimension)) {
coords(n, s) = positions(node, s);
}
}
}
} // akantu

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