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rAKA/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean_inline_impl.cc
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material_neohookean_inline_impl.cc
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/**
* @file material_neohookean_inline_impl.cc
*
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
*
* @date creation: Mon Apr 08 2013
* @date last modification: Sun Oct 19 2014
*
* @brief Implementation of the inline functions of the material elastic
*
* @section LICENSE
*
* Copyright (©) 2014, 2015 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 <iostream>
#include "material_neohookean.hh"
#include <cmath>
#include <utility>
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialNeohookean<dim>::computeDeltaStressOnQuad(
__attribute__((unused)) const Matrix<Real> & grad_u,
__attribute__((unused)) const Matrix<Real> & grad_delta_u,
__attribute__((unused)) Matrix<Real> & delta_S) {}
//! computes the second piola kirchhoff stress, called S
template <UInt dim>
inline void MaterialNeohookean<dim>::computeStressOnQuad(Matrix<Real> & grad_u,
Matrix<Real> & S,
const Real & C33) {
// Neo hookean book
Matrix<Real> F(dim, dim);
Matrix<Real> C(dim, dim); // Right green
Matrix<Real> Cminus(dim, dim); // Right green
this->template gradUToF<dim>(grad_u, F);
this->rightCauchy(F, C);
Real J = F.det() * sqrt(C33); // the term sqrt(C33) corresponds to the off
// plane strain (2D plane stress)
// std::cout<<"det(F) -> "<<J<<std::endl;
Cminus.inverse(C);
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
S(i, j) = (i == j) * mu + (lambda * log(J) - mu) * Cminus(i, j);
}
/* -------------------------------------------------------------------------- */
class C33_NR : public Math::NewtonRaphsonFunctor {
public:
C33_NR(std::string name, const Real & lambda, const Real & mu,
const Matrix<Real> & C)
: NewtonRaphsonFunctor(std::move(name)), lambda(lambda), mu(mu), C(C) {}
inline Real f(Real x) const override {
return (this->lambda / 2. *
(std::log(x) + std::log(this->C(0, 0) * this->C(1, 1) -
Math::pow<2>(this->C(0, 1)))) +
this->mu * (x - 1.));
}
inline Real f_prime(Real x) const override {
AKANTU_DEBUG_ASSERT(std::abs(x) > Math::getTolerance(),
"x is zero (x should be the off plane right Cauchy"
<< " measure in this function so you made a mistake"
<< " somewhere else that lead to a zero here!!!");
return (this->lambda / (2. * x) + this->mu);
}
private:
const Real & lambda;
const Real & mu;
const Matrix<Real> & C;
};
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialNeohookean<dim>::computeThirdAxisDeformationOnQuad(
Matrix<Real> & grad_u, Real & c33_value) {
// Neo hookean book
Matrix<Real> F(dim, dim);
Matrix<Real> C(dim, dim); // Right green
this->template gradUToF<dim>(grad_u, F);
this->rightCauchy(F, C);
Math::NewtonRaphson nr(1e-5, 100);
c33_value = nr.solve(
C33_NR("Neohookean_plan_stress", this->lambda, this->mu, C), c33_value);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void
MaterialNeohookean<dim>::computePiolaKirchhoffOnQuad(const Matrix<Real> & E,
Matrix<Real> & S) {
Real trace = E.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 < dim; ++i)
for (UInt j = 0; j < dim; ++j)
S(i, j) = (i == j) * lambda * trace + 2.0 * mu * E(i, j);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialNeohookean<dim>::computeFirstPiolaKirchhoffOnQuad(
const Matrix<Real> & grad_u, const Matrix<Real> & S, Matrix<Real> & P) {
Matrix<Real> F(dim, dim);
Matrix<Real> C(dim, dim); // Right green
this->template gradUToF<dim>(grad_u, F);
// first Piola-Kirchhoff is computed as the product of the deformation
// gracient
// tensor and the second Piola-Kirchhoff stress tensor
P = F * S;
}
/**************************************************************************************/
/* Computation of the potential energy for a this neo hookean material */
template <UInt dim>
inline void MaterialNeohookean<dim>::computePotentialEnergyOnQuad(
const Matrix<Real> & grad_u, Real & epot) {
Matrix<Real> F(dim, dim);
Matrix<Real> C(dim, dim); // Right green
this->template gradUToF<dim>(grad_u, F);
this->rightCauchy(F, C);
Real J = F.det();
// std::cout<<"det(F) -> "<<J<<std::endl;
epot =
0.5 * lambda * pow(log(J), 2.) + mu * (-log(J) + 0.5 * (C.trace() - dim));
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void MaterialNeohookean<dim>::computeTangentModuliOnQuad(
Matrix<Real> & tangent, Matrix<Real> & grad_u, const Real & C33) {
// Neo hookean book
UInt cols = tangent.cols();
UInt rows = tangent.rows();
Matrix<Real> F(dim, dim);
Matrix<Real> C(dim, dim);
Matrix<Real> Cminus(dim, dim);
this->template gradUToF<dim>(grad_u, F);
this->rightCauchy(F, C);
Real J = F.det() * sqrt(C33);
// std::cout<<"det(F) -> "<<J<<std::endl;
Cminus.inverse(C);
for (UInt m = 0; m < rows; m++) {
UInt i = VoigtHelper<dim>::vec[m][0];
UInt j = VoigtHelper<dim>::vec[m][1];
for (UInt n = 0; n < cols; n++) {
UInt k = VoigtHelper<dim>::vec[n][0];
UInt l = VoigtHelper<dim>::vec[n][1];
// book belytchko
tangent(m, n) = lambda * Cminus(i, j) * Cminus(k, l) +
(mu - lambda * log(J)) * (Cminus(i, k) * Cminus(j, l) +
Cminus(i, l) * Cminus(k, j));
}
}
}
/* -------------------------------------------------------------------------- */
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