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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"
/* -------------------------------------------------------------------------- */
namespace 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>& surface_gradients,
GridHermitian<Real, bdim>& source_stresses,
const Grid<Real, bdim>& wavevectors) const {
using k_out = typename KelvinTrait<T>::out_t;
using m_type = MatrixProxy<Complex, dim, dim>;
using v_type = VectorProxy<const Real, bdim>;
Loop::loop(
[&](typename KelvinTrait<T>::out_t out_local,
MatrixProxy<Complex, dim, dim> surface_gradient,
MatrixProxy<Complex, dim, dim> source_stress,
VectorProxy<const Real, bdim> q) {
// No cutoff
// if (-q.l2norm() * std::abs(y_3) < std::log(cutoff))
// return;
Vector<Real, dim> normal{{{0, 0, 1}}};
auto traction =
el(surface_gradient) * normal; // computing strains from gradu
traction -= source_stress * normal; // subtracting source stresses
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));
},
range<k_out>(out), range<m_type>(surface_gradients),
range<m_type>(source_stresses), range<v_type>(wavevectors));
}
inline void applyConstantTerm(typename KelvinTrait<T>::out_t& out,
Vector<Complex, dim>& /*source*/,
const influence::ElasticHelper<dim>& /*el*/) const {
out = 0;
}
protected:
const T& boussinesq;
const influence::ElasticHelper<dim>& el;
const Real y_3, cutoff;
};
template <>
inline void
MindlinBoussinesqHelper<model_type::volume_2d, influence::Boussinesq<3, 1>>::
applyConstantTerm(
typename KelvinTrait<influence::Boussinesq<3, 1>>::out_t& out,
Vector<Complex, dim>& source,
const influence::ElasticHelper<dim>& el) const {
out = 0;
out(2, 0) = -source(0) / el.mu;
out(2, 1) = -source(1) / el.mu;
out(2, 2) = -source(2) / (el.lambda + 2 * el.mu);
}
} // namespace detail
template <model_type type, UInt order>
void Mindlin<type, order>::applyIf(GridBase<Real>& source, GridBase<Real>& out,
filter_t pred) 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 node, 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);
const Real xi = node * dl;
// this should only be used when node == xi == 0
detail::LinearElement<type, decltype(kelvin_strain)> strain_element{
thrust::make_pair(node, xi), kelvin_strain, source_buffers,
surface_strains, this->wavevectors};
detail::LinearElement<type, decltype(kelvin)> element{
thrust::make_pair(node, xi), kelvin, source_buffers, out_buffer,
this->wavevectors};
out_buffer = 0;
// Simple condition to ensure correct integration
auto filter_out_elem = [&pred](UInt e) {
return not pred(e) and not pred(e + 1);
};
/// Compute surface strains only once (dirty)
if (node == 0) {
surface_strains = 0;
for (UInt e : Loop::range(N - 1)) {
if (filter_out_elem(e))
continue;
const auto node_positions = thrust::make_pair(e * dl, (e + 1) * dl);
strain_element.integrateElement(e, node_positions);
}
}
// Apply Kelvin operator
for (UInt e : Loop::range(N - 1)) {
if (filter_out_elem(e))
continue;
const auto node_positions = thrust::make_pair(e * dl, (e + 1) * dl);
element.integrateElement(e, node_positions);
}
// Correcting for the tractions on the surface
detail::MindlinBoussinesqHelper<type, decltype(boussinesq)> helper(
boussinesq, elasticity, xi, 1e-3);
helper.applyIntegral(out_buffer, surface_strains, source_buffers.front(),
this->wavevectors);
typename detail::KelvinTrait<decltype(boussinesq)>::out_t out_fundamental(
out_buffer(0));
typename detail::KelvinTrait<decltype(kelvin)>::source_t source_fundamental(
source_buffers[node](0));
Vector<Real, trait::dimension> e3;
e3 = 0;
e3(trait::dimension - 1) = -1;
auto in_fundamental = source_fundamental * e3;
// Uniform shift in case of gradient computation
helper.applyConstantTerm(out_fundamental, in_fundamental, elasticity);
};
this->fourierApplyIf(apply, source, out, pred);
}
/* -------------------------------------------------------------------------- */
/* Template instanciation */
/* -------------------------------------------------------------------------- */
template class Mindlin<model_type::volume_2d, 3>;
template class Mindlin<model_type::volume_2d, 4>;
/* -------------------------------------------------------------------------- */
} // namespace tamaas
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