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rAKA/src/model/contact_mechanics/contact_detector.cc
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contact_detector.cc
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/**
* @file contact_detector.cc
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Wed Sep 12 2018
* @date last modification: Fri Sep 21 2018
*
* @brief Mother class for all detection algorithms
*
* @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 "contact_detector.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
ContactDetector::ContactDetector(Mesh & mesh, const ID & id,
const MemoryID & memory_id)
: ContactDetector(mesh, mesh.getNodes(), id, memory_id) {}
/* -------------------------------------------------------------------------- */
ContactDetector::ContactDetector(Mesh & mesh, Array<Real> positions,
const ID & id, const MemoryID & memory_id)
: Memory(id, memory_id), Parsable(ParserType::_contact_detector, id),
mesh(mesh), positions(0, mesh.getSpatialDimension()) {
AKANTU_DEBUG_IN();
this->spatial_dimension = mesh.getSpatialDimension();
this->positions.copy(positions);
this->parseSection();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void ContactDetector::parseSection() {
const Parser & parser = getStaticParser();
const ParserSection & section =
*(parser.getSubSections(ParserType::_contact_detector).first);
auto type = section.getParameterValue<std::string>("type");
if (type == "implicit") {
this->detection_type = _implicit;
} else if (type == "explicit") {
this->detection_type = _explicit;
} else {
AKANTU_ERROR("Unknown detection type : " << type);
}
}
/* -------------------------------------------------------------------------- */
void ContactDetector::search(std::map<UInt, ContactElement> & contact_map) {
this->mesh.fillNodesToElements(this->spatial_dimension - 1);
this->computeMaximalDetectionDistance();
contact_pairs.clear();
SpatialGrid<UInt> master_grid(spatial_dimension);
SpatialGrid<UInt> slave_grid(spatial_dimension);
this->globalSearch(slave_grid, master_grid);
this->localSearch(slave_grid, master_grid);
this->constructContactMap(contact_map);
}
/* -------------------------------------------------------------------------- */
void ContactDetector::globalSearch(SpatialGrid<UInt> & slave_grid,
SpatialGrid<UInt> & master_grid) {
auto & master_list = surface_selector->getMasterList();
auto & slave_list = surface_selector->getSlaveList();
BBox bbox_master(spatial_dimension);
this->constructBoundingBox(bbox_master, master_list);
BBox bbox_slave(spatial_dimension);
this->constructBoundingBox(bbox_slave, slave_list);
auto && bbox_intersection = bbox_master.intersection(bbox_slave);
AKANTU_DEBUG_INFO("Intersection BBox " << bbox_intersection);
Vector<Real> center(spatial_dimension);
bbox_intersection.getCenter(center);
Vector<Real> spacing(spatial_dimension);
this->computeCellSpacing(spacing);
master_grid.setCenter(center);
master_grid.setSpacing(spacing);
this->constructGrid(master_grid, bbox_intersection, master_list);
slave_grid.setCenter(center);
slave_grid.setSpacing(spacing);
this->constructGrid(slave_grid, bbox_intersection, slave_list);
// search slave grid nodes in contactelement array and if they exits
// and still have orthogonal projection on its associated master
// facetremove it from the spatial grid or do not consider it for
// local search, maybe better option will be to have spatial grid of
// type node info and one of the variable of node info should be
// facet already exits
// so contact elements will be updated based on the above
// consideration , this means only those contact elements will be
// keep whose slave node is still in intersection bbox and still has
// projection in its master facet
// also if slave node is already exists in contact element and
// orthogonal projection does not exits then search the associated
// master facets with the current master facets within a given
// radius , this is subjected to computational cost as searching
// neighbbor cells can be more effective.
}
/* -------------------------------------------------------------------------- */
void ContactDetector::localSearch(SpatialGrid<UInt> & slave_grid,
SpatialGrid<UInt> & master_grid) {
// local search
// out of these array check each cell for closet node in that cell
// and neighbouring cells find the actual orthogonally closet
// check the projection of slave node on master facets connected to
// the closet master node, if yes update the contact element with
// slave node and master node and master surfaces connected to the
// master node
// these master surfaces will be needed later to update contact
// elements
/// find the closet master node for each slave node
for (auto && cell_id : slave_grid) {
/// loop over all the slave nodes of the current cell
for (auto && slave_node : slave_grid.getCell(cell_id)) {
bool pair_exists = false;
Vector<Real> pos(spatial_dimension);
for (UInt s : arange(spatial_dimension))
pos(s) = this->positions(slave_node, s);
Real closet_distance = std::numeric_limits<Real>::max();
UInt closet_master_node;
/// loop over all the neighboring cells of the current cell
for (auto && neighbor_cell : cell_id.neighbors()) {
/// loop over the data of neighboring cells from master grid
for (auto && master_node : master_grid.getCell(neighbor_cell)) {
/// check for self contact
if (slave_node == master_node)
continue;
bool is_valid = true;
Array<Element> elements;
this->mesh.getAssociatedElements(slave_node, elements);
for (auto & elem : elements) {
if (elem.kind() != _ek_regular)
continue;
Vector<UInt> connectivity =
const_cast<const Mesh &>(this->mesh).getConnectivity(elem);
auto node_iter = std::find(connectivity.begin(), connectivity.end(),
master_node);
if (node_iter != connectivity.end()) {
is_valid = false;
break;
}
}
Vector<Real> pos2(spatial_dimension);
for (UInt s : arange(spatial_dimension))
pos2(s) = this->positions(master_node, s);
Real distance = pos.distance(pos2);
if (distance <= closet_distance and is_valid) {
closet_master_node = master_node;
closet_distance = distance;
pair_exists = true;
}
}
}
if (pair_exists)
contact_pairs.push_back(std::make_pair(slave_node, closet_master_node));
}
}
}
/* -------------------------------------------------------------------------- */
void ContactDetector::constructContactMap(
std::map<UInt, ContactElement> & contact_map) {
auto surface_dimension = spatial_dimension - 1;
std::map<UInt, ContactElement> previous_contact_map = contact_map;
contact_map.clear();
auto get_connectivity = [&](auto & slave, auto & master) {
Vector<UInt> master_conn =
const_cast<const Mesh &>(this->mesh).getConnectivity(master);
Vector<UInt> elem_conn(master_conn.size() + 1);
elem_conn[0] = slave;
for (UInt i = 1; i < elem_conn.size(); ++i) {
elem_conn[i] = master_conn[i - 1];
}
return elem_conn;
};
for (auto & pairs : contact_pairs) {
const auto & slave_node = pairs.first;
const auto & master_node = pairs.second;
Array<Element> all_elements;
this->mesh.getAssociatedElements(master_node, all_elements);
Array<Element> boundary_elements;
this->filterBoundaryElements(all_elements, boundary_elements);
Array<Real> gaps(boundary_elements.size(), 1, "gaps");
Array<Real> normals(boundary_elements.size(), spatial_dimension, "normals");
Array<Real> projections(boundary_elements.size(), surface_dimension,
"projections");
auto index = this->computeOrthogonalProjection(
slave_node, boundary_elements, normals, gaps, projections);
if (index == UInt(-1)) {
continue;
}
auto connectivity = get_connectivity(slave_node, boundary_elements[index]);
// assign contact element attributes
contact_map[slave_node].setMaster(boundary_elements[index]);
contact_map[slave_node].setGap(gaps[index]);
contact_map[slave_node].setNormal(
Vector<Real>(normals.begin(spatial_dimension)[index], true));
contact_map[slave_node].setProjection(
Vector<Real>(projections.begin(surface_dimension)[index], true));
contact_map[slave_node].setConnectivity(connectivity);
// tangent computation on master surface
Matrix<Real> tangents(surface_dimension, spatial_dimension);
this->computeTangentsOnElement(contact_map[slave_node].master,
contact_map[slave_node].projection,
contact_map[slave_node].normal, tangents);
contact_map[slave_node].setTangent(tangents);
// friction calculation requires history of previous natural
// projection as well as traction
auto search = previous_contact_map.find(slave_node);
if (search != previous_contact_map.end()) {
auto previous_projection =
previous_contact_map[slave_node].getPreviousProjection();
contact_map[slave_node].setPreviousProjection(previous_projection);
auto previous_traction = previous_contact_map[slave_node].getTraction();
contact_map[slave_node].setTraction(previous_traction);
} else {
Vector<Real> previous_projection(surface_dimension, 0.);
contact_map[slave_node].setPreviousProjection(previous_projection);
Vector<Real> previous_traction(surface_dimension, 0.);
contact_map[slave_node].setTraction(previous_traction);
}
// to ensure the self contact between surface does not lead to
// detection of master element which is closet but not
// orthogonally opposite to the slave surface
bool is_valid_self_contact =
this->checkValidityOfSelfContact(slave_node, contact_map[slave_node]);
if (!is_valid_self_contact) {
contact_map.erase(slave_node);
}
}
contact_pairs.clear();
}
/* -------------------------------------------------------------------------- */
UInt ContactDetector::computeOrthogonalProjection(
const UInt & node, const Array<Element> & elements, Array<Real> & normals,
Array<Real> & gaps, Array<Real> & projections) {
Vector<Real> query(spatial_dimension);
for (UInt s : arange(spatial_dimension))
query(s) = this->positions(node, s);
UInt counter = 0;
UInt index = UInt(-1);
Real min_gap = std::numeric_limits<Real>::max();
for (auto && values :
zip(elements, gaps, make_view(normals, spatial_dimension),
make_view(projections, spatial_dimension - 1))) {
const auto & element = std::get<0>(values);
auto & gap = std::get<1>(values);
auto & normal = std::get<2>(values);
auto & projection = std::get<3>(values);
this->computeNormalOnElement(element, normal);
Vector<Real> real_projection(spatial_dimension);
this->computeProjectionOnElement(element, normal, query, projection,
real_projection);
gap = this->computeGap(query, real_projection);
// check if gap is valid or not
// to check this we need normal on master element, vector from
// real projection to slave node, if it is explicit detection
// scheme, we want it to interpenetrate, the dot product should be
// negative and -1.0 and for implciit detection , the dot product
// should be positive and 1.0
bool is_valid = this->checkValidityOfProjection(projection);
auto master_to_slave = query - real_projection;
auto norm = master_to_slave.norm();
if (norm != 0)
master_to_slave /= norm;
Real tolerance = 1e-8;
switch (detection_type) {
case _explicit: {
auto product = master_to_slave.dot(normal);
auto variation = std::abs(product + 1.0);
if (variation <= tolerance and gap <= min_gap and is_valid) {
min_gap = gap;
index = counter;
gap *= -1.0;
}
break;
}
case _implicit: {
auto product = master_to_slave.dot(normal);
auto variation = std::abs(product - 1.0);
if (variation <= tolerance and gap <= min_gap and is_valid) {
min_gap = gap;
index = counter;
gap *= -1.0;
}
}
default:
break;
}
counter++;
}
return index;
}
/* -------------------------------------------------------------------------- */
void ContactDetector::computeProjectionOnElement(
const Element & element, const Vector<Real> & normal,
const Vector<Real> & query, Vector<Real> & natural_projection,
Vector<Real> & real_projection) {
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(element.type);
Matrix<Real> coords(spatial_dimension, nb_nodes_per_element);
this->coordinatesOfElement(element, coords);
Vector<Real> point(coords(0));
Real alpha = (query - point).dot(normal);
real_projection = query - alpha * normal;
this->computeNaturalProjection(element, real_projection, natural_projection);
}
/* -------------------------------------------------------------------------- */
void ContactDetector::computeNaturalProjection(
const Element & element, Vector<Real> & real_projection,
Vector<Real> & natural_projection) {
const ElementType & type = element.type;
UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);
mesh.extractNodalValuesFromElement(this->positions, nodes_coord.storage(),
elem_val +
element.element * nb_nodes_per_element,
nb_nodes_per_element, spatial_dimension);
#define GET_NATURAL_COORDINATE(type) \
ElementClass<type>::inverseMap(real_projection, nodes_coord, \
natural_projection)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NATURAL_COORDINATE);
#undef GET_NATURAL_COORDINATE
}
/* -------------------------------------------------------------------------- */
void ContactDetector::computeTangentsOnElement(const Element & el,
Vector<Real> & projection,
Matrix<Real> & tangents) {
const ElementType & type = el.type;
UInt nb_nodes_master = Mesh::getNbNodesPerElement(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> coords(spatial_dimension, nb_nodes_master);
coordinatesOfElement(el, coords);
tangents.mul<false, true>(shapes_derivatives, coords);
auto temp_tangents = tangents.transpose();
for (UInt i = 0; i < spatial_dimension - 1; ++i) {
auto temp = Vector<Real>(temp_tangents(i));
temp_tangents(i) = temp.normalize();
}
tangents = temp_tangents.transpose();
}
/* -------------------------------------------------------------------------- */
void ContactDetector::computeTangentsOnElement(const Element & el,
Vector<Real> & projection,
Vector<Real> & normal,
Matrix<Real> & tangents) {
const ElementType & type = el.type;
UInt nb_nodes_master = Mesh::getNbNodesPerElement(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> coords(spatial_dimension, nb_nodes_master);
coordinatesOfElement(el, coords);
tangents.mul<false, true>(shapes_derivatives, coords);
auto temp_tangents = tangents.transpose();
for (UInt i = 0; i < spatial_dimension - 1; ++i) {
auto temp = Vector<Real>(temp_tangents(i));
temp_tangents(i) = temp.normalize();
}
tangents = temp_tangents.transpose();
// to ensure that direction of tangents are correct, cross product
// of tangents should give the normal vector computed earlier
switch (spatial_dimension) {
case 2: {
Vector<Real> e_z(3);
e_z[0] = 0.;
e_z[1] = 0.;
e_z[2] = 1.;
Vector<Real> tangent(3);
tangent[0] = tangents(0, 0);
tangent[1] = tangents(0, 1);
tangent[2] = 0.;
auto exp_normal = e_z.crossProduct(tangent);
auto & cal_normal = normal;
auto ddot = cal_normal.dot(exp_normal);
if (ddot < 0) {
tangents *= -1.0;
}
break;
}
case 3: {
auto tang_trans = tangents.transpose();
auto tang1 = Vector<Real>(tang_trans(0));
auto tang2 = Vector<Real>(tang_trans(1));
auto tang1_cross_tang2 = tang1.crossProduct(tang2);
auto exp_normal = tang1_cross_tang2 / tang1_cross_tang2.norm();
auto & cal_normal = normal;
auto ddot = cal_normal.dot(exp_normal);
if (ddot < 0) {
tang_trans(1) *= -1.0;
}
tangents = tang_trans.transpose();
break;
}
default:
break;
}
}
} // namespace akantu
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