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tamaas/src/model/mindlin.cpp
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mindlin.cpp
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2017 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas 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.
*
* Tamaas 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 Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "mindlin.hh"
#include "elasto_plastic_model.hh"
#include "influence.hh"
#include "kelvin_helper.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_TAMAAS__
/* -------------------------------------------------------------------------- */
namespace detail {
template <model_type type, typename T>
class MindlinBoussinesqHelper {
using boussinesq_t = T;
using trait = model_type_traits<type>;
static constexpr UInt dim = trait::dimension;
static constexpr UInt bdim = trait::boundary_dimension;
public:
MindlinBoussinesqHelper(const T& boussinesq,
const influence::ElasticHelper<dim>& el, Real y_3,
Real cutoff)
: boussinesq(boussinesq), el(el), y_3(y_3), cutoff(cutoff) {}
inline void applyIntegral(GridHermitian<Real, bdim>& out,
GridHermitian<Real, bdim>& source,
const Grid<Real, bdim>& wavevectors) const {
Loop::stridedLoop(
[&](typename KelvinTrait<T>::out_t&& out_local,
MatrixProxy<Complex, dim, dim>&& source_local,
VectorProxy<const Real, bdim>&& q) {
// Cutoff
if (-q.l2norm() * std::abs(y_3) < std::log(cutoff))
return;
Vector<Real, dim> normal{{{0, 0, 1}}};
auto traction{el(source_local) * normal};
out_local += boussinesq.applyU0(traction, q) *
influence::KelvinIntegrator<0>::g0<true>(q.l2norm() * y_3);
out_local += (boussinesq.applyU1(traction, q) *
influence::KelvinIntegrator<0>::g1<true>(q.l2norm() * y_3));
},
out, source, wavevectors);
}
protected:
const T& boussinesq;
const influence::ElasticHelper<dim>& el;
const Real y_3, cutoff;
};
} // namespace detail
template <model_type type, UInt order>
void Mindlin<type, order>::apply(GridBase<Real>& source,
GridBase<Real>& out) const {
Real nu = this->model->getPoissonRatio(), mu = this->model->getShearModulus();
constexpr UInt derivative = order - 2;
influence::Kelvin<trait::dimension, derivative> kelvin(mu, nu);
influence::Kelvin<trait::dimension, 2> kelvin_strain(mu, nu);
influence::Boussinesq<trait::dimension, derivative - 1> boussinesq(mu, nu);
influence::ElasticHelper<trait::dimension> elasticity(mu, nu);
auto apply = [&](UInt i, decltype(this->source_buffers)& source_buffers,
decltype(this->disp_buffer)& out_buffer) {
const Real L = this->model->getSystemSize().front();
const UInt N = this->model->getDiscretization().front();
const Real dl = L / (N - 1);
out_buffer = 0;
/// Compute surface strains only once (dirty)
if (i == 0) {
surface_strains = 0;
for (UInt j : Loop::range(N)) {
const Real dij = j * dl;
auto& source = source_buffers[j];
detail::KelvinHelper<type, decltype(kelvin_strain)> helper(
kelvin_strain, dij, dl, 1e-2);
if (j > i) {
helper.template applyIntegral<1>(surface_strains, source,
this->wavevectors);
} else if (j == i) {
helper.template applyIntegral<0>(surface_strains, source,
this->wavevectors);
helper.applyFreeTerm(surface_strains, source, this->wavevectors);
} else {
helper.template applyIntegral<-1>(surface_strains, source,
this->wavevectors);
}
}
}
for (UInt j : Loop::range(N)) {
const Real dij = j * dl - i * dl; // don't factorize!
auto& source = source_buffers[j];
detail::KelvinHelper<type, decltype(kelvin)> helper(
kelvin, dij, dl, 1e-2);
if (j > i) {
helper.template applyIntegral<1>(out_buffer, source, this->wavevectors);
} else if (j == i) {
helper.template applyIntegral<0>(out_buffer, source, this->wavevectors);
helper.applyFreeTerm(out_buffer, source, this->wavevectors);
} else {
helper.template applyIntegral<-1>(out_buffer, source,
this->wavevectors);
}
}
// Correcting for the tractions on the surface
const Real xi = i * dl;
detail::MindlinBoussinesqHelper<type, decltype(boussinesq)> helper(
boussinesq, elasticity, xi, 1e-2);
helper.applyIntegral(out_buffer, surface_strains, this->wavevectors);
// Setting fundamental frequency to zero
typename detail::KelvinTrait<decltype(kelvin)>::out_t out_fundamental(
out_buffer(0));
out_fundamental = 0;
};
this->fourierApply(apply, source, out);
}
/* -------------------------------------------------------------------------- */
/* Template instanciation */
/* -------------------------------------------------------------------------- */
template class Mindlin<model_type::volume_2d, 3>;
template class Mindlin<model_type::volume_2d, 4>;
/* -------------------------------------------------------------------------- */
__END_TAMAAS__
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