void
StructuralFE2Material :: give3dMaterialStiffnessMatrix(FloatMatrix &answer, MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
if ( useNumTangent ) {
// Numerical tangent
StructuralFE2MaterialStatus *status = static_cast<StructuralFE2MaterialStatus*>( this->giveStatus( gp ) );
double h = 1.0e-9;
const FloatArray &epsRed = status->giveTempStrainVector();
FloatArray eps;
StructuralMaterial::giveFullSymVectorForm(eps, epsRed, gp->giveMaterialMode() );
int dim = eps.giveSize();
answer.resize(dim, dim);
answer.zero();
FloatArray sig, sigPert, epsPert;
for(int i = 1; i <= dim; i++) {
// Add a small perturbation to the strain
epsPert = eps;
epsPert.at(i) += h;
giveRealStressVector_3d(sigPert, gp, epsPert, tStep);
answer.setColumn(sigPert, i);
}
giveRealStressVector_3d(sig, gp, eps, tStep);
for(int i = 1; i <= dim; i++) {
for(int j = 1; j <= dim; j++) {
answer.at(j,i) -= sig.at(j);
answer.at(j,i) /= h;
}
}
} else {
StructuralFE2MaterialStatus *ms = static_cast< StructuralFE2MaterialStatus * >( this->giveStatus(gp) );
ms->computeTangent(tStep);
const FloatMatrix &ans9 = ms->giveTangent();
StructuralMaterial::giveReducedSymMatrixForm(answer, ans9, _3dMat);
// const FloatMatrix &ans9 = ms->giveTangent();
// printf("ans9: "); ans9.printYourself();
//
// // Compute the (minor) symmetrized tangent:
// answer.resize(6, 6);
// for ( int i = 0; i < 6; ++i ) {
// for ( int j = 0; j < 6; ++j ) {
// answer(i, j) = ans9(i, j);
// }
// }
// for ( int i = 0; i < 6; ++i ) {
// for ( int j = 6; j < 9; ++j ) {
// answer(i, j-3) += ans9(i, j);
// answer(j-3, i) += ans9(j, i);
// }
// }
// for ( int i = 6; i < 9; ++i ) {
// for ( int j = 6; j < 9; ++j ) {
// answer(j-3, i-3) += ans9(j, i);
// }
// }
// for ( int i = 0; i < 6; ++i ) {
// for ( int j = 3; j < 6; ++j ) {
// answer(j, i) *= 0.5;
// answer(i, j) *= 0.5;
// }
// }
#if 0
// Numerical ATS for debugging
FloatMatrix numericalATS(6, 6);
FloatArray dsig;
// Note! We need a copy of the temp strain, since the pertubations might change it.
FloatArray tempStrain = ms->giveTempStrainVector();
FloatArray sig, strain, sigPert;
giveRealStressVector_3d(sig, gp, tempStrain, tStep);
double hh = 1e-6;
for ( int k = 1; k <= 6; ++k ) {
strain = tempStrain;
strain.at(k) += hh;
giveRealStressVector_3d(sigPert, gp, strain, tStep);
dsig.beDifferenceOf(sigPert, sig);
numericalATS.setColumn(dsig, k);
}
numericalATS.times(1. / hh);
giveRealStressVector_3d(sig, gp, tempStrain, tStep); // Reset
//answer.printYourself("Analytical deviatoric tangent");
//numericalATS.printYourself("Numerical deviatoric tangent");
numericalATS.subtract(answer);
double norm = numericalATS.computeFrobeniusNorm();
if ( norm > answer.computeFrobeniusNorm() * 1e-3 && norm > 0.0 ) {
OOFEM_ERROR("Error in deviatoric tangent");
}
#endif
}
}
void FE2FluidMaterial :: giveStiffnessMatrices(FloatMatrix &dsdd, FloatArray &dsdp, FloatArray &dedd, double &dedp,
MatResponseMode mode, GaussPoint *gp, TimeStep *tStep)
{
FE2FluidMaterialStatus *ms = static_cast< FE2FluidMaterialStatus * >( this->giveStatus(gp) );
ms->computeTangents(tStep);
if ( mode == TangentStiffness ) {
dsdd = ms->giveDeviatoricTangent();
dsdp = ms->giveDeviatoricPressureTangent();
dedd = ms->giveVolumetricDeviatoricTangent();
dedp = ms->giveVolumetricPressureTangent();
#if 0
// Numerical ATS for debugging
FloatMatrix numericalATS(6, 6);
FloatArray dsig;
FloatArray tempStrain(6);
tempStrain.zero();
FloatArray sig, strain, sigPert;
double epspvol;
computeDeviatoricStressVector(sig, epspvol, gp, tempStrain, 0., tStep);
double h = 0.001; // Linear problem, size of this doesn't matter.
for ( int k = 1; k <= 6; ++k ) {
strain = tempStrain;
strain.at(k) += h;
double tmp = strain.at(1) + strain.at(2) + strain.at(3);
strain.at(1) -= tmp/3.0;
strain.at(2) -= tmp/3.0;
strain.at(3) -= tmp/3.0;
strain.printYourself();
computeDeviatoricStressVector(sigPert, epspvol, gp, strain, 0., tStep);
sigPert.printYourself();
dsig.beDifferenceOf(sigPert, sig);
numericalATS.setColumn(dsig, k);
}
numericalATS.times(1. / h);
printf("Analytical deviatoric tangent = ");
dsdd.printYourself();
printf("Numerical deviatoric tangent = ");
numericalATS.printYourself();
numericalATS.subtract(dsdd);
double norm = numericalATS.computeFrobeniusNorm();
if ( norm > dsdd.computeFrobeniusNorm() * DEBUG_ERR && norm > 0.0 ) {
OOFEM_ERROR("Error in deviatoric tangent");
}
#endif
#if 0
// Numerical ATS for debugging
FloatArray strain(3);
strain.zero();
FloatArray sig, sigh;
double epspvol, pressure = 0.0;
double h = 1.00; // Linear problem, size of this doesn't matter.
computeDeviatoricStressVector(sig, epspvol, gp, strain, pressure, tStep);
computeDeviatoricStressVector(sigh, epspvol, gp, strain, pressure + h, tStep);
FloatArray dsigh;
dsigh.beDifferenceOf(sigh, sig);
dsigh.times(1 / h);
printf("Analytical deviatoric pressure tangent = ");
dsdp.printYourself();
printf("Numerical deviatoric pressure tangent = ");
dsigh.printYourself();
dsigh.subtract(dsdp);
double norm = dsigh.computeNorm();
if ( norm > dsdp.computeNorm() * DEBUG_ERR && norm > 0.0 ) {
OOFEM_ERROR("Error in deviatoric pressure tangent");
}
#endif
#if 0
// Numerical ATS for debugging
FloatArray tempStrain(3);
tempStrain.zero();
FloatArray sig, strain;
double epspvol, epspvol11, epspvol22, epspvol12, pressure = 0.0;
double h = 1.0; // Linear problem, size of this doesn't matter.
computeDeviatoricStressVector(sig, epspvol, gp, tempStrain, pressure, tStep);
strain = tempStrain;
strain.at(1) += h;
computeDeviatoricStressVector(sig, epspvol11, gp, strain, pressure, tStep);
strain = tempStrain;
strain.at(2) += h;
computeDeviatoricStressVector(sig, epspvol22, gp, strain, pressure, tStep);
strain = tempStrain;
strain.at(3) += h;
computeDeviatoricStressVector(sig, epspvol12, gp, strain, pressure, tStep);
FloatArray dvol(3);
dvol.at(1) = ( epspvol11 - epspvol ) / h;
dvol.at(2) = ( epspvol22 - epspvol ) / h;
dvol.at(3) = ( epspvol12 - epspvol ) / h;
dvol.at(1) += 1.0;
dvol.at(2) += 1.0;
printf("Analytical volumetric deviatoric tangent = ");
dedd.printYourself();
printf("Numerical volumetric deviatoric tangent = ");
dvol.printYourself();
dvol.subtract(dedd);
double norm = dvol.computeNorm();
if ( norm > dedd.computeNorm() * DEBUG_ERR && norm > 0.0 ) {
OOFEM_ERROR("Error in volumetric deviatoric tangent");
}
#endif
#if 0
// Numerical ATS for debugging
FloatArray strain(3);
strain.zero();
FloatArray sig;
double epspvol, epspvolh, pressure = 0.0;
double h = 1.0; // Linear problem, size of this doesn't matter.
computeDeviatoricStressVector(sig, epspvol, gp, strain, pressure, tStep);
computeDeviatoricStressVector(sig, epspvolh, gp, strain, pressure + h, tStep);
double dvol = -( epspvolh - epspvol ) / h;
printf("Analytical volumetric pressure tangent = %e\n", dedp);
printf("Numerical volumetric pressure tangent = %e\n", dvol);
double norm = fabs(dvol - dedp);
if ( norm > fabs(dedp) * DEBUG_ERR && norm > 0.0 ) {
OOFEM_ERROR("Error in volumetric pressure tangent");
}
#endif
} else {
OOFEM_ERROR("Mode not implemented");
}
}