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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"
/* -------------------------------------------------------------------------- */
__BEGIN_TAMAAS__
/* -------------------------------------------------------------------------- */
namespace influence {
template <UInt dim>
class ElasticHelper {
public:
ElasticHelper(Real mu, Real nu)
: mu(mu), nu(nu), lambda(2 * mu * nu / (1 - 2 * nu)) {}
template <typename ST>
Matrix<Complex, dim, dim>
operator()(StaticMatrix<Complex, ST, dim, dim>& gradu) const {
auto trace{gradu.trace()};
Matrix<Complex, dim, dim> sigma;
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
sigma(i, j) =
(i == j) * lambda * trace + mu * (gradu(i, j) + gradu(j, i));
return sigma;
}
protected:
const Real mu, nu, lambda;
};
template <UInt dim>
class MindlinBoussinesqHelper {
public:
template <typename OutType, typename SourceType, typename BoussType>
static void apply(OutType&& out, SourceType&& source, BoussType&& boussinesq,
const ElasticHelper<dim>& el,
VectorProxy<const Real, dim - 1>& q, Real y_3) {
Vector<Real, dim> normal{{{0, 0, 1}}};
auto traction{el(source) * normal};
out += boussinesq.applyU0(traction, q) *
KelvinIntegrator<0>::g0<true>(q.l2norm() * y_3);
out += (boussinesq.applyU1(traction, q) *
KelvinIntegrator<0>::g1<true>(q.l2norm() * y_3));
}
};
} // namespace influence
template <>
void Mindlin<model_type::volume_2d, 3>::apply(GridBase<Real>& source,
GridBase<Real>& out) const {
Real nu = model->getPoissonRatio(), mu = model->getShearModulus();
influence::Kelvin<trait::dimension, 1> kelvin(mu, nu);
influence::Kelvin<trait::dimension, 2> kelvin_strain(mu, nu);
influence::Boussinesq<trait::dimension, 0> boussinesq(mu, nu);
influence::ElasticHelper<trait::dimension> elasticity(mu, nu);
auto apply = [&](UInt i, decltype(source_buffers)& source_buffers,
decltype(disp_buffer)& displacement) {
constexpr UInt dim = trait::dimension;
const Real L = this->model->getSystemSize().front();
const UInt N = this->model->getDiscretization().front();
const Real dl = L / (N - 1);
// Compute displacements u_i
displacement = 0;
/// Compute surface strains only once (dirty)
if (i == 0) {
surface_strains = 0;
// Computing integral for first element
Loop::stridedLoop(
[&kelvin_strain, dl](MatrixProxy<Complex, dim, dim>&& gradu,
MatrixProxy<Complex, dim, dim>&& f,
VectorProxy<const Real, dim - 1>&& q) {
influence::KelvinIntegrator<1>::integrate<0>(
gradu, f, kelvin_strain, q, 0, dl);
},
surface_strains, source_buffers[0], this->wavevectors);
// Computing integral for rest
for (UInt j = 1; j < N; ++j) {
Real dij = j * dl;
Loop::stridedLoop(
[&kelvin_strain, dij, dl](MatrixProxy<Complex, dim, dim>&& gradu,
MatrixProxy<Complex, dim, dim>&& f,
VectorProxy<const Real, dim - 1>&& q) {
// Cutoff
if (-q.l2norm() * std::abs(dij) < std::log(1e-2))
return;
influence::KelvinIntegrator<1>::integrate<1>(
gradu, f, kelvin_strain, q, dij, dl);
},
surface_strains, source_buffers[j], this->wavevectors);
}
surface_strains *= -1.;
}
// Computing influence of Kelvin kernel
for (UInt j : Loop::range(N)) {
const Real dij = j * dl - i * dl; // don't factorize!
auto& source = source_buffers[j];
#define POTENTIAL(yj_xi) \
Loop::stridedLoop( \
[&kelvin, dij, dl](VectorProxy<Complex, dim>&& u, \
MatrixProxy<Complex, dim, dim>&& f, \
VectorProxy<const Real, dim - 1>&& q) { \
/* Cutoff */ \
if (-q.l2norm() * std::abs(dij) < std::log(1e-2)) \
return; \
influence::KelvinIntegrator<1>::integrate<yj_xi>(u, f, kelvin, q, dij, \
dl); \
}, \
displacement, source, this->wavevectors)
if (j > i) {
POTENTIAL(1);
} else if (j == i) {
POTENTIAL(0);
} else {
POTENTIAL(-1);
}
#undef POTENTIAL
}
// Correcting for the tractions on the surface
Real xi = i * dl;
Loop::stridedLoop(
[&boussinesq, &elasticity, xi](VectorProxy<Complex, dim>&& u,
MatrixProxy<Complex, dim, dim>&& gradu,
VectorProxy<const Real, dim - 1>&& q) {
if (-q.l2norm() * std::abs(xi) < std::log(1e-2))
return;
influence::MindlinBoussinesqHelper<trait::dimension>::apply(
u, gradu, boussinesq, elasticity, q, xi);
},
displacement, surface_strains, this->wavevectors);
// Setting fundamental frequency to zero
VectorProxy<Complex, dim> u_fundamental(displacement(0));
u_fundamental = 0;
};
this->fourierApply(apply, source, out);
}
/* -------------------------------------------------------------------------- */
template <>
void Mindlin<model_type::volume_2d, 4>::apply(GridBase<Real>& source,
GridBase<Real>& out) const {
Real nu = model->getPoissonRatio(), mu = model->getShearModulus();
influence::Kelvin<trait::dimension, 2> kelvin(mu, nu);
influence::Boussinesq<trait::dimension, 1> boussinesq_grad(mu, nu);
influence::ElasticHelper<trait::dimension> elasticity(mu, nu);
auto apply = [&](UInt i, decltype(source_buffers)& source_buffers,
decltype(disp_buffer)& gradu) {
constexpr UInt dim = trait::dimension;
const Real L = this->model->getSystemSize().front();
const UInt N = this->model->getDiscretization().front();
const Real dl = L / (N - 1);
// Compute displacement gradients
gradu = 0;
/// Compute surface strains only once (dirty)
if (i == 0) {
surface_strains = 0;
// Computing integral for first element
Loop::stridedLoop(
[&kelvin, dl](MatrixProxy<Complex, dim, dim>&& gradu,
MatrixProxy<Complex, dim, dim>&& f,
VectorProxy<const Real, dim - 1>&& q) {
influence::KelvinIntegrator<1>::integrate<0>(
gradu, f, kelvin, q, 0, dl);
},
surface_strains, source_buffers[0], this->wavevectors);
// Computing integral for rest
for (UInt j = 1; j < N; ++j) {
Real dij = j * dl;
Loop::stridedLoop(
[&kelvin, dij, dl](MatrixProxy<Complex, dim, dim>&& gradu,
MatrixProxy<Complex, dim, dim>&& f,
VectorProxy<const Real, dim - 1>&& q) {
// Cutoff
if (-q.l2norm() * std::abs(dij) < std::log(1e-2))
return;
influence::KelvinIntegrator<1>::integrate<1>(
gradu, f, kelvin, q, dij, dl);
},
surface_strains, source_buffers[j], this->wavevectors);
}
surface_strains *= -1.;
}
// Computing influence of Kelvin kernel
for (UInt j : Loop::range(N)) {
const Real dij = j * dl - i * dl; // don't factorize!
auto& source = source_buffers[j];
#define POTENTIAL(yj_xi) \
Loop::stridedLoop( \
[&kelvin, dij, dl](MatrixProxy<Complex, dim, dim>&& u, \
MatrixProxy<Complex, dim, dim>&& f, \
VectorProxy<const Real, dim - 1>&& q) { \
/* Cutoff */ \
if (-q.l2norm() * std::abs(dij) < std::log(1e-2)) \
return; \
influence::KelvinIntegrator<1>::integrate<yj_xi>(u, f, kelvin, q, dij, \
dl); \
}, \
gradu, source, this->wavevectors)
if (j > i) {
POTENTIAL(1);
} else if (j == i) {
POTENTIAL(0);
// Additional free term from discontinous Kelvin gradient
Loop::stridedLoop(
[&kelvin](MatrixProxy<Complex, dim, dim>&& u,
MatrixProxy<Complex, dim, dim>&& f,
VectorProxy<const Real, dim - 1>&& q) {
u += kelvin.applyDiscontinuityTerm(q, f);
},
gradu, source, this->wavevectors);
} else {
POTENTIAL(-1);
}
#undef POTENTIAL
}
gradu *= -1.;
// Correcting for the tractions on the surface
Real xi = i * dl;
Loop::stridedLoop(
[&boussinesq_grad, &elasticity,
xi](MatrixProxy<Complex, dim, dim>&& gradu,
MatrixProxy<Complex, dim, dim>&& surface_gradu,
VectorProxy<const Real, dim - 1>&& q) {
if (-q.l2norm() * std::abs(xi) < std::log(1e-2))
return;
influence::MindlinBoussinesqHelper<trait::dimension>::apply(
gradu, surface_gradu, boussinesq_grad, elasticity, q, xi);
},
gradu, surface_strains, this->wavevectors);
// Setting fundamental frequency to zero
MatrixProxy<Complex, dim, dim> gradu_fundamental(gradu(0));
gradu_fundamental = 0;
};
this->fourierApply(apply, source, out);
}
/* -------------------------------------------------------------------------- */
template <model_type type, UInt tensor_order>
void Mindlin<type, tensor_order>::apply(GridBase<Real>& source,
GridBase<Real>& out) const {
TAMAAS_EXCEPTION("The requested operator has not been implemented");
}
/* -------------------------------------------------------------------------- */
/* Template instanciation */
/* -------------------------------------------------------------------------- */
template class Mindlin<model_type::volume_2d, 3>;
template class Mindlin<model_type::volume_2d, 4>;
/* -------------------------------------------------------------------------- */
__END_TAMAAS__

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