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rAKA/model/solid_mechanics/materials/material_mazars_inline_impl.cc
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material_mazars_inline_impl.cc
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/**
* @file material_mazars_inline_impl.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Chambart <marion.chambart@epfl.ch>
* @date Tue Jul 27 11:57:43 2010
*
* @brief Implementation of the inline functions of the material damage
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
inline void MaterialMazars::computeStress(Real * F, Real * sigma, Real & dam) {
Real trace = F[0] + F[4] + F[8];
Real K = 1./3. * (E/(1. - 2.*nu));
Real G = E / (2*(1 + nu));
Real lambda = nu * E / ((1 + nu) * (1 - 2*nu));
Real Fdiag[3];
Real Fdiagp[3];
Math::matrix33_eigenvalues(F, Fdiag);
Fdiagp[0] = std::max(0., Fdiag[0]);
Fdiagp[1] = std::max(0., Fdiag[1]);
Fdiagp[2] = std::max(0., Fdiag[2]);
Real Ehat=sqrt(Fdiagp[0]*Fdiagp[0]+Fdiagp[1]*Fdiagp[1]+Fdiagp[2]*Fdiagp[2]);
sigma[0] = K * trace + 2*G * (F[0] - trace/3);
sigma[4] = K * trace + 2*G * (F[4] - trace/3);
sigma[8] = K * trace + 2*G * (F[8] - trace/3);
sigma[1] = sigma[3] = G * (F[1] + F[3]);
sigma[2] = sigma[6] = G * (F[2] + F[6]);
sigma[5] = sigma[7] = G * (F[5] + F[7]);
Real Fs = Ehat - K0;
if (Fs > 0.) {
Real damt;
Real damc;
damt = 1 - K0*(1 - At)/Ehat - At*(exp(-Bt*(Ehat - K0)));
damc = 1 - K0*(1 - Ac)/Ehat - Ac*(exp(-Bc*(Ehat - K0)));
Real Cdiag;
Cdiag = E*(1-nu)/((1+nu)*(1-2*nu));
Real SigDiag[3];
SigDiag[0] = Cdiag*Fdiag[0] + lambda*(Fdiag[1] + Fdiag[2]);
SigDiag[1] = Cdiag*Fdiag[1] + lambda*(Fdiag[0] + Fdiag[2]);
SigDiag[2] = Cdiag*Fdiag[2] + lambda*(Fdiag[1] + Fdiag[0]);
Real SigDiagT[3];
for (UInt i = 0; i < 3; i++) {
if(SigDiag[i] >= 0.) {
SigDiagT[i] = SigDiag[i];
} else {
SigDiagT[i] = 0.;
}
}
Real TraSigT;
TraSigT = SigDiagT[0] + SigDiagT[1] + SigDiagT[2];
Real FDiagT[3];
for (UInt i = 0; i < 3; i++){
FDiagT [i]= (SigDiagT[i]*(1 + nu) - TraSigT*nu)/E;
}
Real alphat;
alphat = (FDiagT[0]*Fdiagp[0] + FDiagT[1]*Fdiagp[1] + FDiagT[2]*Fdiagp[2])/(Ehat*Ehat);
alphat = std::min(alphat, 1.);
Real alphac;
alphac = 1 - alphat;
Real damtemp;
damtemp = pow(alphat,beta)*damt + pow(alphac,beta)*damc;
dam = std::max(damtemp, dam);
}
dam = std::min(dam,1.);
for(UInt i = 0; i < 9; ++i) sigma[i] *= 1 - dam;
}
/* -------------------------------------------------------------------------- */
inline Real MaterialMazars::celerity() {
return sqrt(E/rho);
}
/* -------------------------------------------------------------------------- */
inline Real MaterialMazars::getStableTimeStep(Real h,
__attribute__ ((unused)) const Element & element) {
return (h/celerity());
}
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