void
GradDpElement :: computeStiffnessMatrix_uk(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
NLStructuralElement *elem = this->giveNLStructuralElement();
double dV;
StructuralCrossSection *cs = elem->giveStructuralCrossSection();
int nlGeo = elem->giveGeometryMode();
FloatArray Nk;
FloatMatrix B, SNk, gPSigma;
answer.clear();
for ( auto &gp: *elem->giveIntegrationRule(0) ) {
GradDpMaterialExtensionInterface *dpmat = dynamic_cast< GradDpMaterialExtensionInterface * >(
cs->giveMaterialInterface(GradDpMaterialExtensionInterfaceType, gp) );
if ( !dpmat ) {
OOFEM_ERROR("Material doesn't implement the required DpGrad interface!");
}
dpmat->givePDGradMatrix_uk(gPSigma, rMode, gp, tStep);
this->computeNkappaMatrixAt(gp, Nk);
elem->computeBmatrixAt(gp, B);
if ( nlGeo == 1 ) {
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else {
elem->computeBHmatrixAt(gp, B);
}
}
dV = elem->computeVolumeAround(gp);
SNk.beProductOf(gPSigma, Nk);
answer.plusProductUnsym(B, SNk, -dV);
}
}
void
GradDpElement :: computeStiffnessMatrix_uu(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
NLStructuralElement *elem = this->giveNLStructuralElement();
StructuralCrossSection *cs = elem->giveStructuralCrossSection();
FloatMatrix B, D, DB;
int nlGeo = elem->giveGeometryMode();
bool matStiffSymmFlag = elem->giveCrossSection()->isCharacteristicMtrxSymmetric(rMode);
answer.clear();
for ( GaussPoint *gp: *elem->giveIntegrationRule(0) ) {
GradDpMaterialExtensionInterface *dpmat = dynamic_cast< GradDpMaterialExtensionInterface * >(
cs->giveMaterialInterface(GradDpMaterialExtensionInterfaceType, gp) );
if ( !dpmat ) {
OOFEM_ERROR("Material doesn't implement the required DpGrad interface!");
}
if ( nlGeo == 0 ) {
elem->computeBmatrixAt(gp, B);
} else if ( nlGeo == 1 ) {
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else {
elem->computeBHmatrixAt(gp, B);
}
}
dpmat->givePDGradMatrix_uu(D, rMode, gp, tStep);
double dV = elem->computeVolumeAround(gp);
DB.beProductOf(D, B);
if ( matStiffSymmFlag ) {
answer.plusProductSymmUpper(B, DB, dV);
} else {
answer.plusProductUnsym(B, DB, dV);
}
}
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
FloatMatrix initialStressMatrix;
elem->computeInitialStressMatrix(initialStressMatrix, tStep);
answer.add(initialStressMatrix);
}
if ( matStiffSymmFlag ) {
answer.symmetrized();
}
}
void
GradDpElement :: giveLocalInternalForcesVector(FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord)
{
NLStructuralElement *elem = this->giveNLStructuralElement();
int nlGeo = elem->giveGeometryMode();
FloatArray BS, vStress;
FloatMatrix B;
for ( GaussPoint *gp: *elem->giveIntegrationRule(0) ) {
if ( nlGeo == 0 || elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else if ( nlGeo == 1 ) {
elem->computeBHmatrixAt(gp, B);
}
vStress = static_cast< StructuralMaterialStatus * >( gp->giveMaterialStatus() )->giveTempStressVector();
if ( vStress.giveSize() == 0 ) { /// @todo is this check really necessary?
break;
}
// Compute nodal internal forces at nodes as f = B^T*Stress dV
double dV = elem->computeVolumeAround(gp);
BS.beTProductOf(B, vStress);
answer.add(dV, BS);
}
}
void
PhaseFieldElement :: computeStiffnessMatrix_ud(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
FloatMatrix B, DB, N_d, DN, S(3,1);
FloatArray stress;
NLStructuralElement *el = this->giveElement();
StructuralCrossSection *cs = dynamic_cast<StructuralCrossSection* > (el->giveCrossSection() );
answer.clear();
for ( auto &gp: el->giveIntegrationRule(0) ) {
StructuralMaterialStatus *matStat = static_cast< StructuralMaterialStatus * >( gp->giveMaterialStatus() );
double dV = el->computeVolumeAround(gp);
// compute int_V ( B^t * D_B * B )dV
this->computeNd_matrixAt(*gp->giveNaturalCoordinates(), N_d);
// stress
FloatArray reducedStrain, a_u;
FloatMatrix B_u;
el->computeBmatrixAt( gp, B_u );
stress = matStat->giveTempStressVector();
stress.times( this->computeGPrim( gp, VM_Total, tStep ) );
S.setColumn(stress,1);
DN.beProductOf(S, N_d);
answer.plusProductUnsym(B_u, DN, dV);
}
}
void
PhaseFieldElement :: computeStiffnessMatrix_uu(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
// This is the regular stiffness matrix times G
FloatMatrix B, DB, N, D_B;
NLStructuralElement *el = this->giveElement();
StructuralCrossSection *cs = dynamic_cast<StructuralCrossSection* > (el->giveCrossSection() );
bool matStiffSymmFlag = cs->isCharacteristicMtrxSymmetric(rMode);
answer.clear();
for ( auto gp: el->giveIntegrationRule(0) ) {
double dV = el->computeVolumeAround(gp);
// compute int_V ( B^t * D_B * B )dV
el->computeBmatrixAt(gp, B );
cs->giveCharMaterialStiffnessMatrix(D_B, rMode, gp, tStep);
D_B.times( computeG(gp, VM_Total, tStep) );
DB.beProductOf(D_B, B);
if ( matStiffSymmFlag ) {
answer.plusProductSymmUpper(B, DB, dV);
} else {
answer.plusProductUnsym(B, DB, dV);
}
}
if ( matStiffSymmFlag ) {
answer.symmetrized();
}
}
void
GradDpElement :: computeLocalStrainVector(FloatArray &answer, GaussPoint *gp, TimeStep *tStep)
{
FloatArray u;
FloatMatrix b;
NLStructuralElement *elem = this->giveNLStructuralElement();
this->computeDisplacementDegreesOfFreedom(u, tStep);
elem->computeBmatrixAt(gp, b);
answer.beProductOf(b, u);
}
void
PhaseFieldElement :: computeBStress_u(FloatArray &answer, GaussPoint *gp, TimeStep *tStep, int useUpdatedGpRecord)
{
// computes G(d)*sig(u)
NLStructuralElement *el = this->giveElement();
FloatArray strain, a_u;
FloatMatrix B_u;
el->computeBmatrixAt(gp, B_u);
this->computeDisplacementUnknowns(a_u, VM_Total, tStep);
strain.beProductOf(B_u, a_u);
el->computeStressVector(answer, strain, gp, tStep);
answer.times( this->computeG(gp, VM_Total, tStep) );
}
void
PhaseFieldElement :: giveInternalForcesVector_u(FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord)
{
// computes int_V ( B_u^t * BSgima_u ) * dV
FloatArray NStress, BStress, vGenStress, NS;
FloatMatrix N, B;
NLStructuralElement *el = this->giveElement();
answer.clear();
for ( auto &gp: el->giveIntegrationRule(0) ) {
double dV = el->computeVolumeAround(gp);
// compute generalized stress measure
el->computeBmatrixAt(gp, B);
this->computeBStress_u(BStress, gp, tStep, useUpdatedGpRecord);
answer.plusProduct(B, BStress, dV);
}
}
void
GradDpElement :: computeStiffnessMatrix_ku(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
double dV;
NLStructuralElement *elem = this->giveNLStructuralElement();
FloatArray Nk;
FloatMatrix B, DkuB, Dku;
StructuralCrossSection *cs = elem->giveStructuralCrossSection();
answer.clear();
int nlGeo = elem->giveGeometryMode();
for ( auto &gp: *elem->giveIntegrationRule(0) ) {
GradDpMaterialExtensionInterface *dpmat = dynamic_cast< GradDpMaterialExtensionInterface * >(
cs->giveMaterialInterface(GradDpMaterialExtensionInterfaceType, gp) );
if ( !dpmat ) {
OOFEM_ERROR("Material doesn't implement the required DpGrad interface!");
}
elem->computeBmatrixAt(gp, B);
if ( nlGeo == 1 ) {
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else {
elem->computeBHmatrixAt(gp, B);
}
}
dpmat->givePDGradMatrix_ku(Dku, rMode, gp, tStep);
this->computeNkappaMatrixAt(gp, Nk);
dV = elem->computeVolumeAround(gp);
DkuB.beProductOf(Dku, B);
answer.plusProductUnsym(Nk, DkuB, -dV);
if ( dpmat->giveAveragingType() == 2 ) {
double dl1, dl2, dl3;
FloatArray Gk;
FloatMatrix D, DB, LDB;
FloatMatrix Bk, BktM22, BktM22Gk, BktM12, BktM12Gk, M22(2, 2), M12(2, 2);
FloatMatrix dL1(1, 3), dL2(1, 3), result1, result2, dLdS, n(2, 2);
this->computeBkappaMatrixAt(gp, Bk);
dpmat->givePDGradMatrix_uu(D, rMode, gp, tStep);
dpmat->givePDGradMatrix_LD(dLdS, rMode, gp, tStep);
this->computeNonlocalGradient(Gk, gp, tStep);
dl1 = dLdS.at(3, 3);
dl2 = dLdS.at(4, 4);
dl3 = dLdS.at(5, 5);
n.at(1, 1) = dLdS.at(1, 1);
n.at(1, 2) = dLdS.at(1, 2);
n.at(2, 1) = dLdS.at(2, 1);
n.at(2, 2) = dLdS.at(2, 2);
// first term Bk^T M22 G L1 D B
// M22 = n2 \otimes n2
M22.at(1, 1) = n.at(1, 2) * n.at(1, 2);
M22.at(1, 2) = n.at(1, 2) * n.at(2, 2);
M22.at(2, 1) = n.at(2, 2) * n.at(1, 2);
M22.at(2, 2) = n.at(2, 2) * n.at(2, 2);
// dL1
dL1.at(1, 1) = dl1 * n.at(1, 1) * n.at(1, 1) + dl2 *n.at(1, 2) * n.at(1, 2);
dL1.at(1, 2) = dl1 * n.at(2, 1) * n.at(2, 1) + dl2 *n.at(2, 2) * n.at(2, 2);
dL1.at(1, 3) = dl1 * n.at(1, 1) * n.at(2, 1) + dl2 *n.at(1, 2) * n.at(2, 2);
DB.beProductOf(D, B);
LDB.beProductOf(dL1, DB);
BktM22.beTProductOf(Bk, M22);
///@todo This can't possibly work if this is uncommented (!) / Mikael
//BktM22Gk.beProductOf(BktM22,Gk);
result1.beProductOf(BktM22Gk, LDB);
answer.add(dV, result1);
// This would be slightly shorter and faster;
//GkLDB.beProductOf(Gk, LDB);
//MGkLDB.beProductOf(M22, GkLDB);
//answer.plusProductUnsym(Bk, MGkLDB, dV);
// M12 + M21 = n1 \otimes n2 + n2 \otimes n1
M12.at(1, 1) = n.at(1, 1) * n.at(1, 2) + n.at(1, 2) * n.at(1, 1);
M12.at(1, 2) = n.at(1, 1) * n.at(2, 2) + n.at(1, 2) * n.at(2, 1);
M12.at(2, 1) = n.at(2, 1) * n.at(1, 2) + n.at(2, 2) * n.at(1, 1);
M12.at(2, 2) = n.at(2, 1) * n.at(2, 2) + n.at(2, 2) * n.at(2, 1);
//dL2
dL2.at(1, 1) = dl3 * ( n.at(1, 1) * n.at(1, 2) + n.at(1, 1) * n.at(1, 2) );
dL2.at(1, 2) = dl3 * ( n.at(2, 1) * n.at(2, 2) + n.at(2, 1) * n.at(2, 2) );
dL2.at(1, 3) = dl3 * ( n.at(1, 2) * n.at(2, 1) + n.at(1, 1) * n.at(2, 2) );
LDB.beProductOf(dL2, DB);
BktM12.beTProductOf(Bk, M12);
///@todo This can't possibly work if this is uncommented (!) / Mikael
//BktM12Gk.beProductOf(BktM12,Gk);
result2.beProductOf(BktM12Gk, LDB);
answer.add(dV, result2);
// This would be slightly shorter and faster;
//GkLDB.beProductOf(Gk, LDB);
//MGkLDB.beProductOf(M12, GkLDB);
//answer.plusProductUnsym(Bk, MGkLDB, dV);
}
}
}
void
GradDpElement :: computeStiffnessMatrix(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
//set displacement and nonlocal location array
this->setDisplacementLocationArray();
this->setNonlocalLocationArray();
NLStructuralElement *elem = this->giveNLStructuralElement();
StructuralCrossSection *cs = elem->giveStructuralCrossSection();
FloatMatrix B, D, DB;
FloatMatrix DkuB, Dku;
FloatArray Nk;
FloatMatrix SNk, gPSigma;
FloatMatrix lStiff;
FloatMatrix Bk, LBk;
FloatMatrix answer_uu, answer_ku, answer_uk, answer_kk;
int nlGeo = elem->giveGeometryMode();
bool matStiffSymmFlag = elem->giveCrossSection()->isCharacteristicMtrxSymmetric(rMode);
for ( auto &gp : *elem->giveIntegrationRule(0) ) {
GradDpMaterialExtensionInterface *dpmat = dynamic_cast< GradDpMaterialExtensionInterface * >(
cs->giveMaterialInterface(GradDpMaterialExtensionInterfaceType, gp) );
if ( !dpmat ) {
OOFEM_ERROR("Material doesn't implement the required DpGrad interface!");
}
double dV = elem->computeVolumeAround(gp);
if ( nlGeo == 0 ) {
elem->computeBmatrixAt(gp, B);
} else if ( nlGeo == 1 ) {
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else {
elem->computeBHmatrixAt(gp, B);
}
}
this->computeNkappaMatrixAt(gp, Nk);
this->computeBkappaMatrixAt(gp, Bk);
dpmat->givePDGradMatrix_uu(D, rMode, gp, tStep);
dpmat->givePDGradMatrix_ku(Dku, rMode, gp, tStep);
dpmat->givePDGradMatrix_uk(gPSigma, rMode, gp, tStep);
dpmat->givePDGradMatrix_kk(lStiff, rMode, gp, tStep);
/////////////////////////////////////////////////////////////////// uu:
DB.beProductOf(D, B);
if ( matStiffSymmFlag ) {
answer_uu.plusProductSymmUpper(B, DB, dV);
} else {
answer_uu.plusProductUnsym(B, DB, dV);
}
//////////////////////////////////////////////////////////////////////// ku:
DkuB.beProductOf(Dku, B);
answer_ku.plusProductUnsym(Nk, DkuB, -dV);
if ( dpmat->giveAveragingType() == 2 ) {
double dl1, dl2, dl3;
FloatMatrix LDB;
FloatMatrix GkLDB, MGkLDB;
FloatMatrix M22, M12;
FloatMatrix dL1(1, 3), dL2(1, 3), dLdS;
FloatArray Gk, n1, n2;
dpmat->givePDGradMatrix_LD(dLdS, rMode, gp, tStep);
this->computeNonlocalGradient(Gk, gp, tStep);
dl1 = dLdS.at(3, 3);
dl2 = dLdS.at(4, 4);
dl3 = dLdS.at(5, 5);
n1 = {dLdS.at(1, 1), dLdS.at(2, 1)};
n2 = {dLdS.at(1, 2), dLdS.at(2, 2)};
// first term Bk^T M22 G L1 D B
// M22 = n2 \otimes n2
M22.plusDyadUnsym(n2, n2, 1.);
// dL1
dL1.at(1, 1) = dl1 * n1.at(1) * n1.at(1) + dl2 * n2.at(1) * n2.at(1);
dL1.at(1, 2) = dl1 * n1.at(2) * n1.at(2) + dl2 * n2.at(2) * n2.at(2);
dL1.at(1, 3) = dl1 * n1.at(1) * n1.at(2) + dl2 * n2.at(1) * n2.at(2);
LDB.beProductOf(dL1, DB);
GkLDB.beProductOf(Gk, LDB);
MGkLDB.beProductOf(M22, GkLDB);
answer.plusProductUnsym(Bk, MGkLDB, dV);
// M12 + M21 = n1 \otimes n2 + n2 \otimes n1
M12.plusDyadUnsym(n1, n2, 1.);
M12.plusDyadUnsym(n2, n1, 1.);
//dL2
dL2.at(1, 1) = dl3 * ( n1.at(1) * n2.at(1) + n1.at(1) * n2.at(1) );
dL2.at(1, 2) = dl3 * ( n1.at(2) * n2.at(2) + n1.at(2) * n2.at(2) );
dL2.at(1, 3) = dl3 * ( n1.at(2) * n2.at(1) + n1.at(1) * n2.at(2) );
// Bk * ((M12 * L2 + M22 * L1) * DB)
LDB.beProductOf(dL2, DB);
GkLDB.beProductOf(Gk, LDB);
MGkLDB.beProductOf(M12, GkLDB);
answer.plusProductUnsym(Bk, MGkLDB, dV);
}
//////////////////////////////////////////////////////////////////////// uk:
SNk.beProductOf(gPSigma, Nk);
answer_uk.plusProductUnsym(B, SNk, -dV); // uk
/////////////////////////////////////////////////////////////////////// kk:
answer_kk.plusProductUnsym(Nk, Nk, dV);
if ( dpmat->giveAveragingType() == 0 || dpmat->giveAveragingType() == 1 ) {
double l = lStiff.at(1, 1);
answer_kk.plusProductUnsym(Bk, Bk, l * l * dV);
} else if ( dpmat->giveAveragingType() == 2 ) {
LBk.beProductOf(lStiff, Bk);
answer_kk.plusProductUnsym(Bk, LBk, dV);
}
}
if ( elem->domain->giveEngngModel()->giveFormulation() == AL ) {
FloatMatrix initialStressMatrix;
elem->computeInitialStressMatrix(initialStressMatrix, tStep);
answer_uu.add(initialStressMatrix);
}
if ( matStiffSymmFlag ) {
answer_uu.symmetrized();
}
answer.resize(totalSize, totalSize);
answer.zero();
answer.assemble(answer_uu, locU);
answer.assemble(answer_uk, locU, locK);
answer.assemble(answer_ku, locK, locU);
answer.assemble(answer_kk,locK);
}
void
GradDpElement :: giveInternalForcesVector(FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord)
{
NLStructuralElement *elem = this->giveNLStructuralElement();
StructuralCrossSection *cs = elem->giveStructuralCrossSection();
FloatArray answerU, answerK;
double localCumulatedStrain = 0.;
FloatMatrix stiffKappa, B;
FloatArray Nk, aux, dKappa, stress;
FloatMatrix lStiff;
FloatMatrix Bk;
FloatArray gKappa, L_gKappa;
//set displacement and nonlocal location array
this->setDisplacementLocationArray();
this->setNonlocalLocationArray();
this->computeNonlocalDegreesOfFreedom(dKappa, tStep);
int nlGeo = elem->giveGeometryMode();
for ( auto &gp: *elem->giveIntegrationRule(0) ) {
GradDpMaterialExtensionInterface *dpmat = dynamic_cast< GradDpMaterialExtensionInterface * >(
cs->giveMaterialInterface(GradDpMaterialExtensionInterfaceType, gp) );
if ( !dpmat ) {
OOFEM_ERROR("Material doesn't implement the required DpGrad interface!");
}
double dV = elem->computeVolumeAround(gp);
if ( nlGeo == 0 || elem->domain->giveEngngModel()->giveFormulation() == AL ) {
elem->computeBmatrixAt(gp, B);
} else if ( nlGeo == 1 ) {
elem->computeBHmatrixAt(gp, B);
}
this->computeStressVectorAndLocalCumulatedStrain(stress, localCumulatedStrain, gp, tStep);
answerU.plusProduct(B, stress, dV);
// Gradient part:
this->computeNkappaMatrixAt(gp, Nk);
this->computeBkappaMatrixAt(gp, Bk);
dpmat->givePDGradMatrix_kk(lStiff, TangentStiffness, gp, tStep);
double kappa = Nk.dotProduct(dKappa);
gKappa.beProductOf(Bk, dKappa);
answerK.add(-dV * localCumulatedStrain, Nk);
answerK.add(kappa * dV, Nk);
if ( dpmat->giveAveragingType() == 0 || dpmat->giveAveragingType() == 1 ) {
double l = lStiff.at(1, 1);
answerK.plusProduct(Bk, gKappa, l * l * dV);
} else if ( dpmat->giveAveragingType() == 2 ) {
L_gKappa.beProductOf(lStiff, gKappa);
answerK.plusProduct(Bk, L_gKappa, dV);
}
}
//this->computeStiffnessMatrix_kk(stiffKappa, TangentStiffness, tStep);
//answerK.beProductOf(stiffKappa, dKappa);
answerK.add(aux);
answer.resize(totalSize);
answer.zero();
answer.assemble(answerU, locU);
answer.assemble(answerK, locK);
}