bool
RerShell :: computeLocalCoordinates(FloatArray &answer, const FloatArray &coords)
{
//set size of return value to 3 area coordinates
answer.resize(3);
//rotate the input point Coordinate System into the element CS
FloatArray inputCoords_ElCS;
this->giveLocalCoordinates( inputCoords_ElCS, const_cast< FloatArray & >(coords) );
//Nodes are defined in the global CS, so they also need to be rotated into the element CS, therefore get the node points and
//rotate them into the element CS
FloatArray nodeCoords;
double x1, x2, x3, y1, y2, y3, z1, z2, z3;
this->giveLocalCoordinates( nodeCoords, * ( this->giveNode(1)->giveCoordinates() ) );
x1 = nodeCoords.at(1);
y1 = nodeCoords.at(2);
z1 = nodeCoords.at(3);
this->giveLocalCoordinates( nodeCoords, * ( this->giveNode(2)->giveCoordinates() ) );
x2 = nodeCoords.at(1);
y2 = nodeCoords.at(2);
z2 = nodeCoords.at(3);
this->giveLocalCoordinates( nodeCoords, * ( this->giveNode(3)->giveCoordinates() ) );
x3 = nodeCoords.at(1);
y3 = nodeCoords.at(2);
z3 = nodeCoords.at(3);
//Compute the area coordinates corresponding to this point
double area;
area = 0.5 * ( x2 * y3 + x1 * y2 + y1 * x3 - x2 * y1 - x3 * y2 - x1 * y3 );
answer.at(1) = ( ( x2 * y3 - x3 * y2 ) + ( y2 - y3 ) * inputCoords_ElCS.at(1) + ( x3 - x2 ) * inputCoords_ElCS.at(2) ) / 2. / area;
answer.at(2) = ( ( x3 * y1 - x1 * y3 ) + ( y3 - y1 ) * inputCoords_ElCS.at(1) + ( x1 - x3 ) * inputCoords_ElCS.at(2) ) / 2. / area;
answer.at(3) = ( ( x1 * y2 - x2 * y1 ) + ( y1 - y2 ) * inputCoords_ElCS.at(1) + ( x2 - x1 ) * inputCoords_ElCS.at(2) ) / 2. / area;
//get midplane location at this point
double midplZ;
midplZ = z1 * answer.at(1) + z2 *answer.at(2) + z3 *answer.at(3);
//check that the z is within the element
StructuralCrossSection *cs = this->giveStructuralCrossSection();
GaussPoint _gp(NULL, 1, new FloatArray ( answer ), 1.0, _2dPlate);
double elthick;
elthick = cs->give(CS_Thickness, & _gp);
if ( elthick / 2.0 + midplZ - fabs( inputCoords_ElCS.at(3) ) < -POINT_TOL ) {
answer.zero();
return false;
}
//check that the point is in the element and set flag
for ( int i = 1; i <= 3; i++ ) {
if ( answer.at(i) < ( 0. - POINT_TOL ) ) {
return false;
}
if ( answer.at(i) > ( 1. + POINT_TOL ) ) {
return false;
}
}
return true;
}
void
PerfectlyPlasticMaterial :: giveRealStressVector(FloatArray &answer,
GaussPoint *gp,
const FloatArray &totalStrain,
TimeStep *atTime)
//
// returns stress vector (in full or reduced form ) of receiver according to
// previous level of stress and current
// strain increment, the only way, how to correctly update gp records
//
//
// may be good idea for nonlinear materials overload this function in order to
// capture strain - stress history for proper modelling receiver behaviour
// and in order to capture possible failure of material
//
// Note: formulated in full stress strain space
{
FloatArray elasticStressIncrement;
FloatArray workStress, *yieldStressGrad, workStress2, stressVector3d;
FloatArray mStrainIncrement3d, mStressElasticIncrement3d, PlasticStrainVector3d;
FloatArray dSigmaIncrement3d, *stressCorrection, *loadingStressGrad;
FloatArray helpArray;
FloatArray plasticStrainIncrement3d, strainIncrement, reducedStrain, reducedStrainIncrement;
FloatArray statusFullStressVector, statusFullPlasticVector;
FloatArray plasticStrainVector;
PerfectlyPlasticMaterialStatus *status = static_cast< PerfectlyPlasticMaterialStatus * >( this->giveStatus(gp) );
FloatMatrix dp;
StructuralCrossSection *crossSection = static_cast< StructuralCrossSection * >
( gp->giveElement()->giveCrossSection() );
double f0, f1, f2, help, dLambda, r, r1, m;
// init temp variables (of YC,LC,Material) at the beginning of step
this->initTempStatus(gp);
// subtract stress independent part
// note: eigenStrains (temperature) is not contained in mechanical strain stored in gp
// therefore it is necessary to subtract always the total eigen strain value
this->giveStressDependentPartOfStrainVector(reducedStrain, gp, totalStrain,
atTime, VM_Total);
reducedStrainIncrement.beDifferenceOf(reducedStrain, status->giveStrainVector());
StructuralMaterial :: giveFullSymVectorForm(strainIncrement, reducedStrainIncrement, gp->giveMaterialMode());
status->givePlasticStrainVector(plasticStrainVector);
StructuralMaterial :: giveFullSymVectorForm(statusFullPlasticVector, plasticStrainVector, gp->giveMaterialMode());
StructuralMaterial :: giveFullSymVectorForm(statusFullStressVector, status->giveStressVector(), gp->giveMaterialMode());
//
// Note : formulated in full stress strain space
//
this->computeTrialStressIncrement(elasticStressIncrement, gp, strainIncrement, atTime);
//
// calculate deltaSigmaPlastic
//
workStress = statusFullStressVector;
workStress.add(elasticStressIncrement);
f0 = this->computeYCValueAt(gp, & statusFullStressVector,
& statusFullPlasticVector);
f1 = this->computeYCValueAt(gp, & workStress,
& statusFullPlasticVector);
PlasticStrainVector3d = statusFullPlasticVector;
if ( f1 >= 0. ) { // loading surface violated by the elastic trial set
if ( f0 < 0. ) { // previously in elastic area
// element not yielding - set the print status
status->setTempYieldFlag(0);
// compute scaling factor
r1 = -f0 / ( f1 - f0 ); // linear interpolation in f (Zienkiewicz, 1969)
yieldStressGrad = this->GiveYCStressGradient(gp, & statusFullStressVector,
& statusFullPlasticVector);
crossSection->imposeStressConstrainsOnGradient(gp, yieldStressGrad);
help = 0.;
for ( int i = 1; i <= 6; i++ ) {
help += yieldStressGrad->at(i) * elasticStressIncrement.at(i);
}
delete yieldStressGrad;
workStress2 = elasticStressIncrement;
workStress2.times(r1);
workStress2.add(statusFullStressVector);
f2 = this->computeYCValueAt(gp, & workStress2,
& statusFullPlasticVector);
if ( fabs(help) > 1.e-6 ) {
r = r1 - f2 / help; // improved value of r (Nayak & Zienkiewicz, 1972)
} else {
r = r1;
}
} else { // f0 should be zero
r = 0.;
}
stressVector3d = elasticStressIncrement;
stressVector3d.times(r);
stressVector3d.add(statusFullStressVector);
m = STRAIN_STEPS;
mStrainIncrement3d = strainIncrement;
mStrainIncrement3d.times( ( 1.0 - r ) / m );
mStressElasticIncrement3d = elasticStressIncrement;
mStressElasticIncrement3d.times( ( 1.0 - r ) / m );
// test if fracture or failure occurs
this->updateIfFailure(gp, & stressVector3d, & PlasticStrainVector3d);
// element yielding - set the print status
status->setTempYieldFlag(1);
// loop over m-steps
for ( int i = 1; i <= m; i++ ) {
// yieldStressGrad = yieldCriteria->
// GiveStressGradient (gp, stressVector3d,
// PlasticStrainVector3d,
// gp-> giveHardeningParam());
// compute dLambda and dp
this->computePlasticStiffnessAt(dp, gp,
& stressVector3d,
& PlasticStrainVector3d,
& mStrainIncrement3d,
atTime,
dLambda);
if ( dLambda < 0. ) {
dLambda = 0.;
}
dSigmaIncrement3d.beProductOf(dp, mStrainIncrement3d);
dSigmaIncrement3d.negated();
dSigmaIncrement3d.add(mStressElasticIncrement3d);
// compute normal to loading surface
loadingStressGrad = this->GiveLCStressGradient(gp, & stressVector3d,
& PlasticStrainVector3d);
// update the stress state
stressVector3d.add(dSigmaIncrement3d);
// compute stress corrections
stressCorrection = this->
GiveStressCorrectionBackToYieldSurface(gp, & stressVector3d,
& PlasticStrainVector3d);
// apply the stress correction -> correction is in the direction of
// the normal to the yield surface
stressVector3d.add(* stressCorrection);
// test = yieldCriteria-> computeValueAt(stressVector3d,
// PlasticStrainVector3d,
// gp-> giveHardeningParam());
// calculate plastic strain increment
crossSection->imposeStrainConstrainsOnGradient(gp, loadingStressGrad);
loadingStressGrad->times(dLambda);
PlasticStrainVector3d.add(* loadingStressGrad);
// strainVector3d -> add (mStrainIncrement3d);
// update yieldCriteria and loading criteria records to newly reached state
// in loadingStressGrad is stored current plastic vector increment
this->updateTempYC(gp, & stressVector3d, & PlasticStrainVector3d);
this->updateTempLC(gp, & stressVector3d, & PlasticStrainVector3d);
// test if fracture or failure occurs
this->updateIfFailure(gp, & stressVector3d, & PlasticStrainVector3d);
delete loadingStressGrad;
delete stressCorrection;
}
// compute total stress increment during strainIncrement
// totalStressIncrement = statusFullStressVector;
// totalStressIncrement.times (-1.0);
// totalStressIncrement.add (stressVector3d);
// update gp
FloatArray helpArry;
StructuralMaterial :: giveReducedSymVectorForm(helpArry, stressVector3d, gp->giveMaterialMode());
status->letTempStressVectorBe(helpArry);
status->letTempStrainVectorBe(totalStrain);
} else {
// element not yielding - set the print status
status->setTempYieldFlag(0);
stressVector3d = statusFullStressVector;
stressVector3d.add(elasticStressIncrement);
// test if fracture or failure occurs
this->updateIfFailure(gp, & stressVector3d, & PlasticStrainVector3d);
// update gp
status->letTempStrainVectorBe(totalStrain);
StructuralMaterial :: giveReducedSymVectorForm(helpArray, stressVector3d, gp->giveMaterialMode());
status->letTempStressVectorBe(helpArray);
}
// update gp plastic strain
plasticStrainIncrement3d.beDifferenceOf(PlasticStrainVector3d, statusFullPlasticVector);
StructuralMaterial :: giveReducedSymVectorForm(helpArray, plasticStrainIncrement3d, gp->giveMaterialMode());
status->letPlasticStrainIncrementVectorBe(helpArray);
StructuralMaterial :: giveReducedSymVectorForm(answer, stressVector3d, gp->giveMaterialMode());
}
void
NLStructuralElement :: computeStiffnessMatrix(FloatMatrix &answer,
MatResponseMode rMode, TimeStep *tStep)
{
StructuralCrossSection *cs = this->giveStructuralCrossSection();
bool matStiffSymmFlag = cs->isCharacteristicMtrxSymmetric(rMode);
answer.clear();
if ( !this->isActivated(tStep) ) {
return;
}
// Compute matrix from material stiffness (total stiffness for small def.) - B^T * dS/dE * B
if ( integrationRulesArray.size() == 1 ) {
FloatMatrix B, D, DB;
for ( auto &gp : *this->giveDefaultIntegrationRulePtr() ) {
// Engineering (small strain) stiffness
if ( nlGeometry == 0 ) {
this->computeBmatrixAt(gp, B);
this->computeConstitutiveMatrixAt(D, rMode, gp, tStep);
} else if ( nlGeometry == 1 ) {
if ( this->domain->giveEngngModel()->giveFormulation() == AL ) { // Material stiffness dC/de
this->computeBmatrixAt(gp, B);
/// @todo We probably need overloaded function (like above) here as well.
cs->giveStiffnessMatrix_dCde(D, rMode, gp, tStep);
} else { // Material stiffness dP/dF
this->computeBHmatrixAt(gp, B);
/// @todo We probably need overloaded function (like above) here as well.
cs->giveStiffnessMatrix_dPdF(D, rMode, gp, tStep);
}
}
double dV = this->computeVolumeAround(gp);
DB.beProductOf(D, B);
if ( matStiffSymmFlag ) {
answer.plusProductSymmUpper(B, DB, dV);
} else {
answer.plusProductUnsym(B, DB, dV);
}
}
if ( this->domain->giveEngngModel()->giveFormulation() == AL ) {
FloatMatrix initialStressMatrix;
this->computeInitialStressMatrix(initialStressMatrix, tStep);
answer.add(initialStressMatrix);
}
} else { /// @todo Verify that it works with large deformations
if ( this->domain->giveEngngModel()->giveFormulation() == AL ) {
OOFEM_ERROR("Updated lagrangian not supported yet");
}
int iStartIndx, iEndIndx, jStartIndx, jEndIndx;
FloatMatrix Bi, Bj, D, Dij, DBj;
for ( int i = 0; i < (int)integrationRulesArray.size(); i++ ) {
iStartIndx = integrationRulesArray [ i ]->getStartIndexOfLocalStrainWhereApply();
iEndIndx = integrationRulesArray [ i ]->getEndIndexOfLocalStrainWhereApply();
for ( int j = 0; j < (int)integrationRulesArray.size(); j++ ) {
IntegrationRule *iRule;
jStartIndx = integrationRulesArray [ j ]->getStartIndexOfLocalStrainWhereApply();
jEndIndx = integrationRulesArray [ j ]->getEndIndexOfLocalStrainWhereApply();
if ( i == j ) {
iRule = integrationRulesArray [ i ].get();
} else if ( integrationRulesArray [ i ]->giveNumberOfIntegrationPoints() < integrationRulesArray [ j ]->giveNumberOfIntegrationPoints() ) {
iRule = integrationRulesArray [ i ].get();
} else {
iRule = integrationRulesArray [ j ].get();
}
for ( GaussPoint *gp: *iRule ) {
// Engineering (small strain) stiffness dSig/dEps
if ( nlGeometry == 0 ) {
this->computeBmatrixAt(gp, Bi, iStartIndx, iEndIndx);
this->computeConstitutiveMatrixAt(D, rMode, gp, tStep);
} else if ( nlGeometry == 1 ) {
if ( this->domain->giveEngngModel()->giveFormulation() == AL ) { // Material stiffness dC/de
this->computeBmatrixAt(gp, Bi);
cs->giveStiffnessMatrix_dCde(D, rMode, gp, tStep);
} else { // Material stiffness dP/dF
this->computeBHmatrixAt(gp, Bi);
cs->giveStiffnessMatrix_dPdF(D, rMode, gp, tStep);
}
}
if ( i != j ) {
if ( nlGeometry == 0 ) {
this->computeBmatrixAt(gp, Bj, jStartIndx, jEndIndx);
} else if ( nlGeometry == 1 ) {
if ( this->domain->giveEngngModel()->giveFormulation() == AL ) {
this->computeBmatrixAt(gp, Bj);
} else {
this->computeBHmatrixAt(gp, Bj);
}
}
} else {
Bj = Bi;
}
Dij.beSubMatrixOf(D, iStartIndx, iEndIndx, jStartIndx, jEndIndx);
double dV = this->computeVolumeAround(gp);
DBj.beProductOf(Dij, Bj);
if ( matStiffSymmFlag ) {
answer.plusProductSymmUpper(Bi, DBj, dV);
} else {
answer.plusProductUnsym(Bi, DBj, dV);
}
}
}
}
}
if ( matStiffSymmFlag ) {
answer.symmetrized();
}
}
void
PerfectlyPlasticMaterial :: computePlasticStiffnessAt(FloatMatrix &answer,
GaussPoint *gp,
FloatArray *currentStressVector,
FloatArray *currentPlasticStrainVector,
FloatArray *strainIncrement3d,
TimeStep *atTime,
double &lambda)
//
// Computes full form of Plastic stiffness Matrix at given state.
// gp is used only and only for setting proper MaterialMode ()
// returns proportionality factor lambda also if strainIncrement3d != NULL
{
StructuralCrossSection *crossSection = static_cast< StructuralCrossSection * >
( gp->giveElement()->giveCrossSection() );
FloatMatrix de, *yeldStressGradMat, *loadingStressGradMat;
FloatMatrix fsde, gsfsde;
FloatArray *yeldStressGrad, *loadingStressGrad;
FloatArray help;
double denominator, nominator;
int i;
//
// force de to be elastic even if gp in plastic state
// to do this, a flag in this class exist -> ForceElasticResponce
// if this flag is set to nonzero, function this::Give3dMaterialStiffnessMatrix
// will be forced to return only elasticPart of 3dMaterialStiffnessMatrix
// This function also set the ForceElasticFlagResponce to zero.
//
this->giveEffectiveMaterialStiffnessMatrix(de, TangentStiffness, gp, atTime);
yeldStressGrad = this->GiveYCStressGradient(gp, currentStressVector,
currentPlasticStrainVector);
crossSection->imposeStressConstrainsOnGradient(gp, yeldStressGrad);
yeldStressGradMat = new FloatMatrix(yeldStressGrad, 1); // transpose
loadingStressGrad = this->GiveLCStressGradient(gp, currentStressVector,
currentPlasticStrainVector);
crossSection->imposeStrainConstrainsOnGradient(gp, loadingStressGrad);
loadingStressGradMat = new FloatMatrix(yeldStressGrad);
help.beProductOf(de, * loadingStressGrad);
delete loadingStressGrad;
fsde.beProductOf(* yeldStressGradMat, de);
delete yeldStressGradMat;
gsfsde.beProductOf(* loadingStressGradMat, fsde);
delete loadingStressGradMat;
denominator = 0.;
for ( i = 1; i <= 6; i++ ) {
denominator += yeldStressGrad->at(i) * help.at(i);
}
answer.beProductOf(de, gsfsde);
answer.times( -( 1. / denominator ) );
if ( strainIncrement3d != NULL ) { // compute proportional factor lambda
nominator = 0.;
help.beProductOf(de, * strainIncrement3d);
for ( i = 1; i <= 6; i++ ) {
nominator += yeldStressGrad->at(i) * help.at(i);
}
lambda = nominator / denominator;
}
delete yeldStressGrad;
}
