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material_vreepeerlings_inline_impl.hh
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material_vreepeerlings_inline_impl.hh
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/**
* @file material_vreepeerlings_inline_impl.hh
*
* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
*
*
* @brief Specialization of the material class for the VreePeerlings material
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
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 {
AKANTU_ERROR("This instruction here was commented but has to be checked");
// 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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