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material_neohookean.cc
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/**
* @file material_neohookean.cc
*
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Apr 08 2013
* @date last modification: Thu Feb 20 2020
*
* @brief Specialization of the material class for finite deformation
* neo-hookean material
*
*
* @section LICENSE
*
* Copyright (©) 2014-2021 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 "material_neohookean.hh"
#include "solid_mechanics_model.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
MaterialNeohookean<spatial_dimension>::MaterialNeohookean(
SolidMechanicsModel & model, const ID & id)
: PlaneStressToolbox<spatial_dimension>(model, id) {
AKANTU_DEBUG_IN();
this->registerParam("E", E, Real(0.), _pat_parsable | _pat_modifiable,
"Young's modulus");
this->registerParam("nu", nu, Real(0.5), _pat_parsable | _pat_modifiable,
"Poisson's ratio");
this->registerParam("lambda", lambda, _pat_readable,
"First Lamé coefficient");
this->registerParam("mu", mu, _pat_readable, "Second Lamé coefficient");
this->registerParam("kapa", kpa, _pat_readable, "Bulk coefficient");
this->finite_deformation = true;
this->initialize_third_axis_deformation = true;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialNeohookean<spatial_dimension>::initMaterial() {
AKANTU_DEBUG_IN();
PlaneStressToolbox<spatial_dimension>::initMaterial();
if (spatial_dimension == 1) {
nu = 0.;
}
this->updateInternalParameters();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <> void MaterialNeohookean<2>::initMaterial() {
AKANTU_DEBUG_IN();
PlaneStressToolbox<2>::initMaterial();
this->updateInternalParameters();
if (this->plane_stress) {
this->third_axis_deformation.setDefaultValue(1.);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialNeohookean<spatial_dimension>::updateInternalParameters() {
lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
mu = E / (2 * (1 + nu));
kpa = lambda + 2. / 3. * mu;
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialNeohookean<dim>::computeCauchyStressPlaneStress(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
PlaneStressToolbox<dim>::computeCauchyStressPlaneStress(el_type, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <>
void MaterialNeohookean<2>::computeCauchyStressPlaneStress(
ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
auto gradu_it = this->gradu(el_type, ghost_type).begin(2, 2);
auto gradu_end = this->gradu(el_type, ghost_type).end(2, 2);
auto piola_it = this->piola_kirchhoff_2(el_type, ghost_type).begin(2, 2);
auto stress_it = this->stress(el_type, ghost_type).begin(2, 2);
auto c33_it = this->third_axis_deformation(el_type, ghost_type).begin();
for (; gradu_it != gradu_end; ++gradu_it, ++piola_it, ++stress_it, ++c33_it) {
Matrix<Real> & grad_u = *gradu_it;
Matrix<Real> & piola = *piola_it;
Matrix<Real> & sigma = *stress_it;
StoCauchy<2>(gradUToF<2>(grad_u), piola, sigma, *c33_it);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialNeohookean<dim>::computeStress(ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
computeStressOnQuad(grad_u, sigma);
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <>
void MaterialNeohookean<2>::computeStress(ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
if (this->plane_stress) {
PlaneStressToolbox<2>::computeStress(el_type, ghost_type);
auto c33_it = this->third_axis_deformation(el_type, ghost_type).begin();
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
computeStressOnQuad(grad_u, sigma, *c33_it);
++c33_it;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
} else {
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
computeStressOnQuad(grad_u, sigma);
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void MaterialNeohookean<dim>::computeThirdAxisDeformation(
ElementType /*el_type*/, GhostType /*ghost_type*/) {}
/* -------------------------------------------------------------------------- */
template <>
void MaterialNeohookean<2>::computeThirdAxisDeformation(ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(this->plane_stress, "The third component of the strain "
"can only be computed for 2D "
"problems in Plane Stress!!");
Array<Real>::scalar_iterator c33_it =
this->third_axis_deformation(el_type, ghost_type).begin();
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
computeThirdAxisDeformationOnQuad(grad_u, *c33_it);
++c33_it;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialNeohookean<spatial_dimension>::computePotentialEnergy(
ElementType el_type) {
AKANTU_DEBUG_IN();
Material::computePotentialEnergy(el_type);
Array<Real>::scalar_iterator epot = this->potential_energy(el_type).begin();
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);
computePotentialEnergyOnQuad(grad_u, *epot);
++epot;
MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialNeohookean<spatial_dimension>::computeTangentModuli(
__attribute__((unused)) ElementType el_type, Array<Real> & tangent_matrix,
__attribute__((unused)) GhostType ghost_type) {
AKANTU_DEBUG_IN();
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
computeTangentModuliOnQuad(tangent, grad_u);
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <>
void MaterialNeohookean<2>::computeTangentModuli(__attribute__((unused))
ElementType el_type,
Array<Real> & tangent_matrix,
__attribute__((unused))
GhostType ghost_type) {
AKANTU_DEBUG_IN();
if (this->plane_stress) {
PlaneStressToolbox<2>::computeStress(el_type, ghost_type);
Array<Real>::const_scalar_iterator c33_it =
this->third_axis_deformation(el_type, ghost_type).begin();
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
computeTangentModuliOnQuad(tangent, grad_u, *c33_it);
++c33_it;
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;
} else {
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
computeTangentModuliOnQuad(tangent, grad_u);
MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
Real MaterialNeohookean<spatial_dimension>::getPushWaveSpeed(
__attribute__((unused)) const Element & element) const {
return sqrt((this->lambda + 2 * this->mu) / this->rho);
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
Real MaterialNeohookean<spatial_dimension>::getShearWaveSpeed(
__attribute__((unused)) const Element & element) const {
return sqrt(this->mu / this->rho);
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(neohookean, MaterialNeohookean);
} // namespace akantu

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