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rAKA/src/material_vreepeerlings_inline_impl.cc
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material_vreepeerlings_inline_impl.cc
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/**
* @file material_vreepeerlings_inline_impl.cc
*
* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
*
* @date Fri Feb 24 14:27:15 2012
*
* @brief Specialization of the material class for the VreePeerlings material
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension, template <UInt> class MatParent>
inline void
MaterialVreePeerlings<spatial_dimension, MatParent>::computeStressOnQuad(Matrix<Real> & grad_u,
Matrix<Real> & sigma,
Real & dam,
Real & Equistrain,
Real & Equistrain_rate,
Real & Kapaq,
Real dt,
Matrix<Real> & strain_rate_vrplgs,
Real & FullDam_ValStrain,
Real & FullDam_ValStrain_rate,
Real & Nb_damage) {
Real I1=0.; /// trace initialization of the strain tensor
Real J2=0.; /// J2 [J2=1/6(3 strain:strain - I1*I1)] initialization
Real I1rate=0.; /// trace initialization of the strain rate tensor
Real J2rate=0.; /// J2 [J2=1/3(3 strain:strainrate - I1*I1rate)] initialization
if (spatial_dimension == 1){
I1 = grad_u.trace();
J2 = .5*grad_u(0,0)*grad_u(0,0) - I1 * I1/6.;
I1rate = strain_rate_vrplgs.trace();
J2rate = grad_u(0,0)*strain_rate_vrplgs(0,0) -I1 * I1rate/6.;
}
else {
// if(this->plane_stress) {
// Real tmp = this->nu/(this->nu - 1);
// tmp *= tmp;
// I1 = (grad_u(0,0) + grad_u(1,1))*(1 - 2*this->nu)/(1 - this->nu);
// J2 = .5*(grad_u(0,0)*grad_u(0,0) +
// grad_u(1,1)*grad_u(1,1) +
// tmp*(grad_u(0,0) + grad_u(1,1))*(grad_u(0,0) + grad_u(1,1)) +
// .5*(grad_u(0,1) + grad_u(1,0))*(grad_u(0,1) + grad_u(1,0))) -
// I1*I1/6.;
// I1rate = (strain_rate_vrplgs(0,0) + strain_rate_vrplgs(1,1))*(1 - 2*this->nu)/(1 - this->nu);
// J2rate = (grad_u(0,0)*strain_rate_vrplgs(0,0) +
// grad_u(1,1)*strain_rate_vrplgs(1,1) +
// tmp*(grad_u(0,0) + grad_u(1,1))*(strain_rate_vrplgs(0,0) + strain_rate_vrplgs(1,1)) +
// (grad_u(0,1)*strain_rate_vrplgs(1,0)) + (grad_u(0,1)*strain_rate_vrplgs(1,0))) -
// I1*I1rate/3.;
// }
// else {
I1 = grad_u.trace();
for(UInt i=0; i<spatial_dimension; ++i )
for(UInt j=i; j<spatial_dimension; ++j )
J2 += 0.5*( (i==j)*grad_u(i,i)*grad_u(i,i) +0.5*(1- (i==j))*( (grad_u(i,j) + grad_u(j,i))*(grad_u(i,j) + grad_u(j,i)) ));
J2-= I1 * I1/6.;
I1rate = strain_rate_vrplgs.trace();
bool is3D= spatial_dimension==3;
J2rate = (grad_u(0,0)*strain_rate_vrplgs(0,0) +
grad_u(1,1)*strain_rate_vrplgs(1,1) +
is3D * grad_u(2,2)*strain_rate_vrplgs(2,2) +
(grad_u(0,1)*strain_rate_vrplgs(1,0)) + (grad_u(0,1)*strain_rate_vrplgs(1,0)) +
is3D * (grad_u(1,2)*strain_rate_vrplgs(2,1)) + is3D * (grad_u(1,2)*strain_rate_vrplgs(2,1)) +
is3D * (grad_u(2,0)*strain_rate_vrplgs(0,2)) + is3D * (grad_u(2,0)*strain_rate_vrplgs(0,2))) -
I1 * I1rate/3.;
// }
}
Real tmp_1 = (Kct - 1)/(1 - 2*this->nu);
Real tmp_2 = (12 * Kct)/((1 + this->nu)*(1 + this->nu));
Equistrain = tmp_1 * I1 / (2*Kct) + 1./(2*Kct) * std::sqrt(tmp_1*tmp_1*I1*I1 + tmp_2*J2);
if(I1 * I1rate > 0 || J2rate > 0){
Equistrain_rate =tmp_1 * std::abs(I1rate) / (2*Kct) + 1./(4*Kct)*(2*tmp_1*tmp_1*I1*I1rate + tmp_2*J2rate) / std::sqrt(tmp_1*tmp_1*I1*I1 + tmp_2*J2);
}else{
Equistrain_rate = Equistrain_rate;
}
if(!this->is_non_local) {
computeDamageAndStressOnQuad(sigma, dam, Equistrain, Equistrain_rate, Kapaq, dt, FullDam_ValStrain, FullDam_ValStrain_rate, Nb_damage);
}
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension, template <UInt> class MatParent>
inline void
MaterialVreePeerlings<spatial_dimension, MatParent>::computeDamageAndStressOnQuad(Matrix<Real> & sigma,
Real & dam,
Real & Equistrain,
Real & Equistrain_rate,
Real & Kapaq,
Real dt,
Real & FullDam_ValStrain,
Real & FullDam_ValStrain_rate,
Real & Nb_damage) {
//---------------------------------------------------------------------------------------
// rate-dependence model
//
//---------------------------------------------------------------------------------------
Real Kapao = Crate*(1.+(std::pow(std::abs(Equistrain_rate)*Arate,Brate)))*(1.-Kapao_randomness) + Kapao_randomness*Kapaq;
Real Kapac_99 = Kapac*.99;
Real Kapaodyn = 0;
if (Kapao > Kapaoi) {
if (Kapao < Kapac_99) {
Kapaodyn = Kapao;
} else {
Kapaodyn = Kapac_99;
}
} else {
Kapaodyn = Kapaoi;
}
Real Fd1 = Equistrain - Kapaoi;
if (Fd1 > 0)
{
Real dam1 = 1. - Kapaodyn/Equistrain * ((Kapac - Equistrain)/(Kapac - Kapaodyn));
if (dam1 > dam){
dam = std::min(dam1,1.);
Nb_damage = Nb_damage + 1.;
if (dam >= 1.){
FullDam_ValStrain = Equistrain;
FullDam_ValStrain_rate = Equistrain_rate;
}
}
}
//---------------------------------------------------------------------------------------
// delayed damage (see Marions thesis page 68)
//---------------------------------------------------------------------------------------
// Real viscosity = 10.;
// Real damRateInfini = 10000000.;
// Real gequi = 1. - Kapaq/Equistrain * ((Kapac-Equistrain)/(Kapac - Kapaq));
// if (gequi - dam > 0){
//
// Real damRate = damRateInfini * (1. - std::exp(-1*viscosity * (gequi - dam)));
// if (damrate > 0){
//
// if (dam < 1.){
// dam = dam + damRate*dt;
// } else {
// dam = 1.;
// }
// }
// }
//
//---------------------------------------------------------------------------------------
sigma *= 1-dam;
}
/* -------------------------------------------------------------------------- */
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