void
IDGMaterial :: give1dStressStiffMtrx(FloatMatrix &answer, MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
IsotropicDamageMaterialStatus *status = static_cast< IsotropicDamageMaterialStatus * >( this->giveStatus(gp) );
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double om;
om = status->giveTempDamage();
om = min(om, maxOmega);
answer.resize(1, 1);
answer.at(1, 1) = lmat->give('E', gp);
answer.times(1.0 - om);
}
void
MisesMatGrad :: give1dKappaMatrix(FloatMatrix &answer, MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
answer.resize(1, 1);
answer.zero();
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double E = lmat->give('E', gp);
MisesMatGradStatus *status = static_cast< MisesMatGradStatus * >( this->giveStatus(gp) );
double tempKappa = status->giveTempCumulativePlasticStrain();
double dKappa = tempKappa - status->giveCumulativePlasticStrain();
const FloatArray &effStress = status->giveTempEffectiveStress();
double stress = effStress.at(1);
if ( dKappa > 0 ) {
double trialS = signum(stress);
double factor = trialS * E / ( E + H );
answer.at(1, 1) = factor;
}
}
void
IDGMaterial :: give1dGprime(FloatMatrix &answer, MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
IDGMaterialStatus *status = static_cast< IDGMaterialStatus * >( this->giveStatus(gp) );
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double damage = status->giveDamage();
double tempDamage = status->giveTempDamage();
double E = lmat->give('E', gp);
answer.resize(1, 1);
if ( tempDamage > damage ) {
double nlKappa = status->giveNonlocalCumulatedStrain();
answer.at(1, 1) = E * status->giveTempStrainVector().at(1);
double gPrime = damageFunctionPrime(nlKappa, gp);
answer.times(gPrime);
} else {
answer.zero();
}
}
void
MisesMatNl :: giveRemoteNonlocalStiffnessContribution(GaussPoint *gp, IntArray &rloc, const UnknownNumberingScheme &s,
FloatArray &rcontrib, TimeStep *atTime)
{
int ncols, nsize, i, j;
double sum, kappa, tempKappa;
MisesMatNlStatus *status = ( MisesMatNlStatus * ) this->giveStatus(gp);
StructuralElement *elem = ( StructuralElement * )( gp->giveElement() );
FloatMatrix b;
FloatArray stress;
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double E = lmat->give('E', gp);
elem->giveLocationArray(rloc, EID_MomentumBalance, s);
elem->computeBmatrixAt(gp, b);
ncols = b.giveNumberOfColumns();
rcontrib.resize(ncols);
kappa = status->giveCumulativePlasticStrain();
tempKappa = status->giveTempCumulativePlasticStrain();
if ( ( tempKappa - kappa ) > 0 ) {
status->giveTempEffectiveStress(stress);
if ( gp->giveMaterialMode() == _1dMat ) {
nsize = stress.giveSize();
double coeff = sgn( stress.at(1) ) * E / ( E + H );
for ( i = 1; i <= ncols; i++ ) {
sum = 0.;
for ( j = 1; j <= nsize; j++ ) {
sum += stress.at(j) * coeff * b.at(j, i);
}
rcontrib.at(i) = sum;
}
}
} else {
rcontrib.zero();
}
}
void
MisesMatGrad :: give1dStressStiffMtrx(FloatMatrix &answer, MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
answer.resize(1, 1);
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double E = lmat->give('E', gp);
answer.at(1, 1) = E;
if ( mode != TangentStiffness ) {
return;
}
MisesMatGradStatus *status = static_cast< MisesMatGradStatus * >( this->giveStatus(gp) );
double tempKappa = status->giveTempCumulativePlasticStrain();
// increment of cumulative plastic strain as an indicator of plastic loading
double dKappa = ( tempKappa - status->giveCumulativePlasticStrain() );
/********************************************************************/
double tempDamage = status->giveTempDamage();
double damage = status->giveDamage();
/*********************************************************************/
double nlKappa = status->giveNonlocalCumulatedStrain();
double kappa = mParam * nlKappa + ( 1. - mParam ) * tempKappa;
if ( dKappa <= 0.0 ) {
answer.at(1, 1) = ( 1. - tempDamage ) * E;
return;
}
// === plastic loading ===
const FloatArray &stressVector = status->giveTempEffectiveStress();
double stress = stressVector.at(1);
answer.at(1, 1) = ( 1. - tempDamage ) * E * H / ( E + H );
if ( ( tempDamage - damage ) > 0 ) {
answer.at(1, 1) = answer.at(1, 1) - ( 1. - mParam ) * computeDamageParamPrime(kappa) * E / ( E + H ) * signum(stress) * stress;
}
}
void
MisesMat :: performPlasticityReturn(GaussPoint *gp, const FloatArray &totalStrain)
{
MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) );
double kappa;
FloatArray plStrain;
FloatArray fullStress;
// get the initial plastic strain and initial kappa from the status
plStrain = status->givePlasticStrain();
kappa = status->giveCumulativePlasticStrain();
// === radial return algorithm ===
if ( totalStrain.giveSize() == 1 ) {
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double E = lmat->give('E', gp);
/*trial stress*/
fullStress.resize(6);
fullStress.at(1) = E * ( totalStrain.at(1) - plStrain.at(1) );
double trialS = fabs(fullStress.at(1));
/*yield function*/
double yieldValue = trialS - (sig0 + H * kappa);
// === radial return algorithm ===
if ( yieldValue > 0 ) {
double dKappa = yieldValue / ( H + E );
kappa += dKappa;
plStrain.at(1) += dKappa * signum( fullStress.at(1) );
plStrain.at(2) -= 0.5 * dKappa * signum( fullStress.at(1) );
plStrain.at(3) -= 0.5 * dKappa * signum( fullStress.at(1) );
fullStress.at(1) -= dKappa * E * signum( fullStress.at(1) );
}
} else {
// elastic predictor
FloatArray elStrain = totalStrain;
elStrain.subtract(plStrain);
FloatArray elStrainDev;
double elStrainVol;
elStrainVol = computeDeviatoricVolumetricSplit(elStrainDev, elStrain);
FloatArray trialStressDev;
applyDeviatoricElasticStiffness(trialStressDev, elStrainDev, G);
/**************************************************************/
double trialStressVol = 3 * K * elStrainVol;
/**************************************************************/
// store the deviatoric and trial stress (reused by algorithmic stiffness)
status->letTrialStressDevBe(trialStressDev);
status->setTrialStressVol(trialStressVol);
// check the yield condition at the trial state
double trialS = computeStressNorm(trialStressDev);
double yieldValue = sqrt(3./2.) * trialS - (sig0 + H * kappa);
if ( yieldValue > 0. ) {
// increment of cumulative plastic strain
double dKappa = yieldValue / ( H + 3. * G );
kappa += dKappa;
FloatArray dPlStrain;
// the following line is equivalent to multiplication by scaling matrix P
applyDeviatoricElasticCompliance(dPlStrain, trialStressDev, 0.5);
// increment of plastic strain
plStrain.add(sqrt(3. / 2.) * dKappa / trialS, dPlStrain);
// scaling of deviatoric trial stress
trialStressDev.times(1. - sqrt(6.) * G * dKappa / trialS);
}
// assemble the stress from the elastically computed volumetric part
// and scaled deviatoric part
computeDeviatoricVolumetricSum(fullStress, trialStressDev, trialStressVol);
}
// store the effective stress in status
status->letTempEffectiveStressBe(fullStress);
// store the plastic strain and cumulative plastic strain
status->letTempPlasticStrainBe(plStrain);
status->setTempCumulativePlasticStrain(kappa);
}
// returns the stress vector in 3d stress space
// computed from the previous plastic strain and current total strain
void
MisesMat :: performPlasticityReturn(GaussPoint *gp, const FloatArray &totalStrain)
{
double kappa, yieldValue, dKappa;
FloatArray reducedStress;
FloatArray strain, plStrain;
MaterialMode mode = gp->giveMaterialMode();
MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) );
StressVector fullStress(mode);
this->initTempStatus(gp);
this->initGpForNewStep(gp);
// get the initial plastic strain and initial kappa from the status
status->givePlasticStrain(plStrain);
kappa = status->giveCumulativePlasticStrain();
// === radial return algorithm ===
if ( mode == _1dMat ) {
LinearElasticMaterial *lmat = this->giveLinearElasticMaterial();
double E = lmat->give('E', gp);
/*trial stress*/
fullStress.at(1) = E * ( totalStrain.at(1) - plStrain.at(1) );
double sigmaY = sig0 + H * kappa;
double trialS = fullStress.at(1);
trialS = fabs(trialS);
/*yield function*/
yieldValue = trialS - sigmaY;
// === radial return algorithm ===
if ( yieldValue > 0 ) {
dKappa = yieldValue / ( H + E );
kappa += dKappa;
fullStress.at(1) = fullStress.at(1) - dKappa *E *signum( fullStress.at(1) );
plStrain.at(1) = plStrain.at(1) + dKappa *signum( fullStress.at(1) );
}
} else if ( ( mode == _PlaneStrain ) || ( mode == _3dMat ) ) {
// elastic predictor
StrainVector elStrain(totalStrain, mode);
elStrain.subtract(plStrain);
StrainVector elStrainDev(mode);
double elStrainVol;
elStrain.computeDeviatoricVolumetricSplit(elStrainDev, elStrainVol);
StressVector trialStressDev(mode);
elStrainDev.applyDeviatoricElasticStiffness(trialStressDev, G);
/**************************************************************/
double trialStressVol;
trialStressVol = 3 * K * elStrainVol;
/**************************************************************/
// store the deviatoric and trial stress (reused by algorithmic stiffness)
status->letTrialStressDevBe(trialStressDev);
status->setTrialStressVol(trialStressVol);
// check the yield condition at the trial state
double trialS = trialStressDev.computeStressNorm();
double sigmaY = sig0 + H * kappa;
yieldValue = sqrt(3. / 2.) * trialS - sigmaY;
if ( yieldValue > 0. ) {
// increment of cumulative plastic strain
dKappa = yieldValue / ( H + 3. * G );
kappa += dKappa;
StrainVector dPlStrain(mode);
// the following line is equivalent to multiplication by scaling matrix P
trialStressDev.applyDeviatoricElasticCompliance(dPlStrain, 0.5);
// increment of plastic strain
dPlStrain.times(sqrt(3. / 2.) * dKappa / trialS);
plStrain.add(dPlStrain);
// scaling of deviatoric trial stress
trialStressDev.times(1. - sqrt(6.) * G * dKappa / trialS);
}
// assemble the stress from the elastically computed volumetric part
// and scaled deviatoric part
double stressVol = 3. * K * elStrainVol;
trialStressDev.computeDeviatoricVolumetricSum(fullStress, stressVol);
}
// store the effective stress in status
status->letTempEffectiveStressBe(fullStress);
// store the plastic strain and cumulative plastic strain
status->letTempPlasticStrainBe(plStrain);
status->setTempCumulativePlasticStrain(kappa);
}