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rAKA/extra_packages/igfem/src/material_igfem/material_igfem_elastic_inline_impl.hh
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material_igfem_elastic_inline_impl.hh
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/**
* @file material_igfem_elastic_inline_impl.hh
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief Implementation of the inline functions of the material igfem elastic
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
inline void MaterialIGFEMElastic<spatial_dimension>::computeStressOnQuad(
const Matrix<Real> & grad_u, Matrix<Real> & sigma, const Real lambda,
const Real mu) const {
Real trace = grad_u.trace(); // trace = (\nabla u)_{kk}
// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
// u_{ij} + \nabla u_{ji})
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
sigma(i, j) =
(i == j) * lambda * trace + mu * (grad_u(i, j) + grad_u(j, i));
}
}
}
/* -------------------------------------------------------------------------- */
template <>
inline void MaterialIGFEMElastic<1>::computeStressOnQuad(
const Matrix<Real> & grad_u, Matrix<Real> & sigma, const Real lambda,
const Real mu) const {
sigma(0, 0) = 2 * mu * grad_u(0, 0);
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
inline void MaterialIGFEMElastic<spatial_dimension>::computeTangentModuliOnQuad(
Matrix<Real> & tangent, const Real lambda, const Real mu) const {
UInt n = tangent.cols();
// Real Ep = E/((1+nu)*(1-2*nu));
Real Miiii = lambda + 2 * mu;
Real Miijj = lambda;
Real Mijij = mu;
if (spatial_dimension == 1)
tangent(0, 0) = 3 * mu;
else
tangent(0, 0) = Miiii;
// test of dimension should by optimized out by the compiler due to the
// template
if (spatial_dimension >= 2) {
tangent(1, 1) = Miiii;
tangent(0, 1) = Miijj;
tangent(1, 0) = Miijj;
tangent(n - 1, n - 1) = Mijij;
}
if (spatial_dimension == 3) {
tangent(2, 2) = Miiii;
tangent(0, 2) = Miijj;
tangent(1, 2) = Miijj;
tangent(2, 0) = Miijj;
tangent(2, 1) = Miijj;
tangent(3, 3) = Mijij;
tangent(4, 4) = Mijij;
}
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialIGFEMElastic<dim>::computePotentialEnergyOnQuad(
const Matrix<Real> & grad_u, const Matrix<Real> & sigma, Real & epot) {
AKANTU_DEBUG_TO_IMPLEMENT();
/// epot = .5 * sigma.doubleDot(grad_u);
}
/* -------------------------------------------------------------------------- */
template <>
inline void MaterialIGFEMElastic<1>::computeTangentModuliOnQuad(
Matrix<Real> & tangent, const Real lambda, const Real mu) const {
tangent(0, 0) = 2 * mu;
}
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