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hertz_3D.cc
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hertz_3D.cc
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/**
* @file hertz_3D.cc
*
* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
*
* @date Fri Apr 4 11:30:00 2014
*
* @brief File used to obtain 3D implicit contact results and compare with
* Hertz theory
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 <chrono>
#include "contact_impl.hh"
using namespace akantu;
using std::cout;
using std::endl;
using std::setw;
using std::setprecision;
int main(int argc, char *argv[]) {
// set dimension
static const UInt dim = 3;
// type definitions
typedef Point<dim> point_type;
typedef BoundingBox<dim> bbox_type;
typedef SolidMechanicsModel model_type;
typedef Contact<dim, MasterAssignator,
SelectResolution<_static, _augmented_lagrangian> >
contact_type;
typedef std::chrono::high_resolution_clock clock;
typedef std::chrono::seconds seconds;
clock::time_point t0 = clock::now();
initialize("steel.dat", argc, argv);
// create mesh
Mesh mesh(dim);
// read mesh
mesh.read("hertz_3D.msh");
// create model
model_type model(mesh);
SolidMechanicsModelOptions opt(_static);
// initialize material
model.initFull(opt);
// create data structure that holds contact data
contact_type cd(argc, argv, model);
// optimal value of penalty multiplier
cd[Alpha] = 0.05;
cd[Multiplier_tol] = 1.e-2;
cd[Newton_tol] = 1.e-2;
cd[Verbose] = true;
// set Paraview output resluts
model.setBaseName("contact");
model.addDumpFieldVector("displacement");
// call update current position to be able to call later
// the function to get current positions
model.updateCurrentPosition();
// get physical names from Gmsh file
mesh.createGroupsFromMeshData<std::string>("physical_names");
// set-up bounding box to include slave nodes that lie inside it
Real l1 = 1.;
Real l2 = 0.2;
Real l3 = 1.;
point_type c1(-l1 / 2, -l2 / 2, -l3 / 2);
point_type c2(l1 / 2, l2 / 2, l3 / 2);
bbox_type bb(c1, c2);
// get areas for the nodes of the circle
// this is done by applying a unit pressure to the contact surface elements
model.applyBC(BC::Neumann::FromHigherDim(Matrix<Real>::eye(3, 1.)),
"contact_surface");
Array<Real> &areas = model.getForce();
// loop over contact surface nodes and store node areas
ElementGroup &eg = mesh.getElementGroup("contact_surface");
Array<Real> &coords = mesh.getNodes();
cout << "- Adding areas to slave nodes. " << endl;
for (auto nit = eg.node_begin(); nit != eg.node_end(); ++nit) {
point_type p(&coords(*nit));
// ignore slave node if it doesn't lie within the bounding box
if (!(bb & p))
continue;
cd.addSlave(*nit);
// compute area contributing to the slave node
Real a = 0.;
for (UInt i = 0; i < dim; ++i)
a += pow(areas(*nit, i), 2.);
cd.addArea(*nit, sqrt(a));
}
// set force value to zero
areas.clear();
// add master surface to find pairs
cd.searchSurface("rigid_surface");
// apply boundary conditions for the rigid plane
model.applyBC(BC::Dirichlet::FixedValue(0., _x), "bottom_body");
model.applyBC(BC::Dirichlet::FixedValue(0., _y), "bottom_body");
model.applyBC(BC::Dirichlet::FixedValue(0., _z), "bottom_body");
// block z-disp in extreme points of top surface
model.getBlockedDOFs()(1, 2) = true;
model.getBlockedDOFs()(2, 2) = true;
// block x-disp in extreme points of top surface
model.getBlockedDOFs()(3, 0) = true;
model.getBlockedDOFs()(4, 0) = true;
const size_t steps = 30;
Real data[3][steps]; // store results for printing
Real step = 0.001; // top displacement increment
size_t k = 0;
for (Real delta = 0; delta <= step * steps; delta += step) {
// apply displacement to the top surface of the half-sphere
model.applyBC(BC::Dirichlet::FixedValue(-delta, _y), "top_surface");
// solve contact step, this function also dumps Paraview files
solveContactStep<_uzawa>(cd);
// solveContactStep<_generalized_newton>(cd);
data[0][k] = delta;
data[1][k] = cd.getForce();
data[2][k] = cd.getMaxPressure();
++k;
}
// print results
size_t w = 14;
cout << setprecision(4);
cout << endl << setw(w) << "Disp." << setw(w) << "Force" << setw(w)
<< "Max pressure" << endl;
for (size_t i = 0; i < steps; ++i)
cout << setw(w) << data[0][i] << setw(w) << data[1][i] << setw(w)
<< data[2][i] << endl;
clock::time_point t1 = clock::now();
seconds total_s = std::chrono::duration_cast<seconds>(t1 - t0);
cout << "*** INFO *** Simulation took " << total_s.count() << " s" << endl;
// finalize simulation
finalize();
return EXIT_SUCCESS;
}

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