void
MisesMat :: give1dStressStiffMtrx(FloatMatrix &answer,
MatResponseMode mode,
GaussPoint *gp,
TimeStep *tStep)
{
this->giveLinearElasticMaterial()->give1dStressStiffMtrx(answer, mode, gp, tStep);
MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) );
double kappa = status->giveCumulativePlasticStrain();
// increment of cumulative plastic strain as an indicator of plastic loading
double tempKappa = status->giveTempCumulativePlasticStrain();
double omega = status->giveTempDamage();
double E = answer.at(1, 1);
if ( mode != TangentStiffness ) {
return;
}
if ( tempKappa <= kappa ) { // elastic loading - elastic stiffness plays the role of tangent stiffness
answer.times(1 - omega);
return;
}
// === plastic loading ===
const FloatArray &stressVector = status->giveTempEffectiveStress();
double stress = stressVector.at(1);
answer.resize(1, 1);
answer.at(1, 1) = ( 1 - omega ) * E * H / ( E + H ) - computeDamageParamPrime(tempKappa) * E / ( E + H ) * stress * signum(stress);
}
// returns the consistent (algorithmic) tangent stiffness matrix
void
MisesMat :: give3dSSMaterialStiffnessMatrix(FloatMatrix &answer,
MatResponseMode mode,
GaussPoint *gp,
TimeStep *atTime)
{
// start from the elastic stiffness
this->giveLinearElasticMaterial()->give3dMaterialStiffnessMatrix(answer, mode, gp, atTime);
if ( mode != TangentStiffness ) {
return;
}
MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) );
double kappa = status->giveCumulativePlasticStrain();
double tempKappa = status->giveTempCumulativePlasticStrain();
// increment of cumulative plastic strain as an indicator of plastic loading
double dKappa = tempKappa - kappa;
if ( dKappa <= 0.0 ) { // elastic loading - elastic stiffness plays the role of tangent stiffness
return;
}
// === plastic loading ===
// yield stress at the beginning of the step
double sigmaY = sig0 + H * kappa;
// trial deviatoric stress and its norm
StressVector trialStressDev(_3dMat);
double trialStressVol;
status->giveTrialStressVol(trialStressVol);
status->giveTrialStressDev(trialStressDev);
double trialS = trialStressDev.computeStressNorm();
// one correction term
FloatMatrix stiffnessCorrection(6, 6);
stiffnessCorrection.beDyadicProductOf(trialStressDev, trialStressDev);
double factor = -2. * sqrt(6.) * G * G / trialS;
double factor1 = factor * sigmaY / ( ( H + 3. * G ) * trialS * trialS );
stiffnessCorrection.times(factor1);
answer.add(stiffnessCorrection);
// another correction term
stiffnessCorrection.bePinvID();
double factor2 = factor * dKappa;
stiffnessCorrection.times(factor2);
answer.add(stiffnessCorrection);
//influence of damage
// double omega = computeDamageParam(tempKappa);
double omega = status->giveTempDamage();
answer.times(1. - omega);
FloatArray effStress;
status->giveTempEffectiveStress(effStress);
double omegaPrime = computeDamageParamPrime(tempKappa);
double scalar = -omegaPrime *sqrt(6.) * G / ( 3. * G + H ) / trialS;
stiffnessCorrection.beDyadicProductOf(effStress, trialStressDev);
stiffnessCorrection.times(scalar);
answer.add(stiffnessCorrection);
}
