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hertz_2D.cc
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hertz_2D.cc
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/**
* @file hertz_2D.cc
*
* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
*
* @date creation: Tue May 13 2014
* @date last modification: Fri Sep 19 2014
*
* @brief This file tests for the Hertz solution in 2D
*
* @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/>.
*
*/
#include "contact_impl.hh"
#include "dumpable_inline_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 = 2;
// type definitions
typedef Point<dim> point_type;
typedef BoundingBox<dim> bbox_type;
typedef SolidMechanicsModel model_type;
typedef ModelElement<model_type> master_type;
typedef Contact <dim, MasterAssignator, SelectResolution <_static, _augmented_lagrangian> >
contact_type;
initialize("steel.dat", argc, argv);
// create mesh
Mesh mesh(dim);
// read mesh
mesh.read("hertz_2D.msh");
// create model
model_type model(mesh);
SolidMechanicsModelOptions opt(_static);
// initialize material
model.initFull(opt);
model.updateCurrentPosition();
// create data structure that holds contact data
contact_type cd(argc, argv, model);
// optimal value of penalty multiplier
cd[Alpha] = 0.4;
// set Paraview output resluts
model.setBaseName("contact");
model.addDumpFieldVector("displacement");
// use bounding box to minimize slave-master pairs
Real r0 = 0.5;
Real r1 = 0.15;
point_type c1(-r0/2,-r1/2);
point_type c2( r0/2, r1/2);
bbox_type bb(c1, c2);
// get physical names from mesh
Array<Real> &coords = mesh.getNodes();
mesh.createGroupsFromMeshData<std::string>("physical_names");
// compute areas for slave nodes that are used for the computation of contact pressures
model.applyBC(BC::Neumann::FromHigherDim(Matrix<Real>::eye(2,1.)), "contact_surface");
// NOTE: the areas are computed by assigning a unit pressure to the contact surface,
// then the magnitude of the resulting force vector at nodes gives its associated area
Array<Real>& areas = model.getForce();
// add slave-master pairs and store slave node areas
ElementGroup &eg = mesh.getElementGroup("contact_surface");
ElementGroup &rs = mesh.getElementGroup("rigid");
for (auto nit = eg.node_begin(); nit != eg.node_end(); ++nit) {
// get point of slave node
point_type n(&coords(*nit));
// process only if within bounding box
if (bb & n) {
// loop over element types
for (ElementGroup::type_iterator tit = rs.firstType(); tit != rs.lastType(); ++tit)
// loop over elements of the rigid surface
for (ElementGroup::const_element_iterator it = rs.element_begin(*tit);
it != rs.element_end(*tit); ++it) {
// create master element
master_type m(model, _segment_2, *it);
assert(has_projection(n,m.point<2>(0),m.point<2>(1)));
// add slave-master pair
cd.addPair(*nit,m);
}
// compute and add area to slave node
Real a = 0.;
for (UInt i=0; i<dim; ++i)
a += pow(areas(*nit, i),2.);
cd.addArea(*nit, sqrt(a));
}
}
// clear force vector before the start of the simulation
areas.clear();
// output contact data info
cout<<cd;
// apply boundary conditions
model.applyBC(BC::Dirichlet::FixedValue(0., _x), "rigid");
model.applyBC(BC::Dirichlet::FixedValue(0., _y), "rigid");
model.getBlockedDOFs()(7,0) = true;
Real data[3][50]; // store results for printing
Real step = 0.001; // top displacement increment
Real Delta = 0.05; // maximum imposed displacement
size_t k=0;
// loop over displacement increments
for (Real delta = step; delta <= Delta+step; delta += step) {
// apply displacement at the top
model.applyBC(BC::Dirichlet::FixedValue(-delta, _y), "top");
// solve contact step (no need to call solve on the model object)
solveContactStep<_uzawa>(cd);
data[0][k] = delta;
data[1][k] = cd.getForce();
data[2][k] = cd.getMaxPressure();
++k;
}
// print results
size_t w = 10;
cout<<setprecision(2);
cout<<setw(w)<<"\nDisp."<<setw(w)<<"Force"<<setw(w)<<"Max pressure"<<endl;
for (int i=0; i<50; ++i)
cout<<setw(w)<<data[0][i]<<setw(w)<<data[1][i]<<setw(w)<<data[2][i]<<endl;
// finalize simulation
finalize();
return EXIT_SUCCESS;
}

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