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phasefield_exponential.hh
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/**
* @file phasefield_exponential.hh
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Fri Jun 18 2020
* @date last modification: Mon Jan 29 2020
*
* @brief Phasefield law for approximating discrete crack as an exponential
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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 "aka_common.hh"
#include "phasefield.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_PHASEFIELD_EXPONENTIAL_HH__
#define __AKANTU_PHASEFIELD_EXPONENTIAL_HH__
namespace akantu {
class PhaseFieldExponential : public PhaseField {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
PhaseFieldExponential(PhaseFieldModel & model, const ID & id = "" );
~PhaseFieldExponential() override = default;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
protected:
void computePhiOnQuad(const Matrix<Real> &, Real &, Real &);
void computeDrivingForce(const ElementType & , GhostType ) override;
inline void computeDrivingForceOnQuad(const Real &, Real &);
inline void computeDamageEnergyDensityOnQuad(const Real &, Real &);
public:
void updateInternalParameters() override;
};
/* -------------------------------------------------------------------------- */
inline void PhaseFieldExponential:: computeDrivingForceOnQuad(const Real & phi_quad,
Real & driving_force_quad){
driving_force_quad = 2.0 * phi_quad;
}
/* -------------------------------------------------------------------------- */
inline void PhaseFieldExponential::computeDamageEnergyDensityOnQuad(const Real & phi_quad,
Real & dam_energy_quad) {
dam_energy_quad = 2.0 * phi_quad + this->g_c/this->l0;
}
/* -------------------------------------------------------------------------- */
inline void PhaseFieldExponential::computePhiOnQuad(const Matrix<Real> & strain_quad,
Real & phi_quad, Real & phi_hist_quad) {
Matrix<Real> strain_plus(spatial_dimension, spatial_dimension);
Matrix<Real> strain_minus(spatial_dimension, spatial_dimension);
Matrix<Real> strain_dir(spatial_dimension, spatial_dimension);
Matrix<Real> strain_diag_plus(spatial_dimension, spatial_dimension);
Matrix<Real> strain_diag_minus(spatial_dimension, spatial_dimension);
Vector<Real> strain_values(spatial_dimension);
Real trace_plus, trace_minus;
strain_plus.zero();
strain_minus.zero();
strain_dir.zero();
strain_values.zero();
strain_diag_plus.zero();
strain_diag_minus.zero();
strain_quad.eig(strain_values, strain_dir);
for (UInt i = 0; i < spatial_dimension; i++) {
strain_diag_plus(i, i) = std::max(Real(0.), strain_values(i));
strain_diag_minus(i, i) = std::min(Real(0.), strain_values(i));
}
Matrix<Real> mat_tmp(spatial_dimension, spatial_dimension);
Matrix<Real> sigma_plus(spatial_dimension, spatial_dimension);
Matrix<Real> sigma_minus(spatial_dimension, spatial_dimension);
mat_tmp.mul<false, true>(strain_diag_plus, strain_dir);
strain_plus.mul<false, false>(strain_dir, mat_tmp);
mat_tmp.mul<false, true>(strain_diag_minus, strain_dir);
strain_minus.mul<false, true>(strain_dir, mat_tmp);
trace_plus = std::max(Real(0.), strain_quad.trace());
trace_minus = std::min(Real(0.), strain_quad.trace());
for (UInt i = 0; i < spatial_dimension; i++) {
for (UInt j = 0; j < spatial_dimension; j++) {
sigma_plus(i, j) =
(i == j) * lambda * trace_plus + 2 * mu * strain_plus(i, j);
sigma_minus(i, j) =
(i == j) * lambda * trace_minus + 2 * mu * strain_minus(i, j);
}
}
phi_quad = 0.5 * sigma_plus.doubleDot(strain_quad);
if (phi_quad < phi_hist_quad)
phi_quad = phi_hist_quad;
}
}
#endif

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