void
RCM2Material :: giveCrackedStiffnessMatrix(FloatMatrix &answer,
MatResponseMode rMode,
GaussPoint *gp,
TimeStep *atTime)
//
//
// Returns material incremental stiffness matrix for cracked concrete.
// This matrix is composed from submatrix, each of them corresponds to
// one active crack in material point.
// when constructing submatrix, following assumptions are made:
//
// A salient characteriastic of crack formation concerns the fact that in most general case
// of tree-dimensional solid only 3 out of 6 components of the crack strain rate vector
// are possibly non-zero.(the normal and two shear strain rates).
// We therefore assume that the stress-strain law for the crack has a structure
// such that the other strains rate components vanish. Moreover we assume that
// the novanishing strain rate components are only related to corresponding
// stress rate components (submatrix has dimensions 3x3).
//
// if strainIncrement is defined (not null) then we take care about possible unlo&reloading
// we don't teke care about possible cracking (or non-linear softening) during strain increment
// this correction is made in this -> updateCrackStatus (gp);
{
RCM2MaterialStatus *status = ( RCM2MaterialStatus * ) this->giveStatus(gp);
int i;
int numberOfActiveCracks = status->giveNumberOfTempActiveCracks();
IntArray crackMap;
status->giveCrackMap(crackMap);
if ( numberOfActiveCracks == 0 ) {
answer.resize(0, 0);
return;
}
answer.resize(3, 3);
answer.zero();
// loop over each active crack plane
for ( i = 1; i <= 3; i++ ) {
if ( crackMap.at(i) ) {
// obtain incremental law for one crack
answer.at(i, i) = this->giveCrackingModulus(rMode, gp,
status->giveCrackStrain(i),
i);
}
}
}
void
RCM2Material :: giveEffectiveMaterialStiffnessMatrix(FloatMatrix &answer,
MatResponseForm form,
MatResponseMode rMode, GaussPoint *gp,
TimeStep *atTime)
//
// returns effective material stiffness matrix in full form
// for gp stress strain mode
//
{
RCM2MaterialStatus *status = ( RCM2MaterialStatus * ) this->giveStatus(gp);
StructuralMaterial *lMat = static_cast< StructuralMaterial * >( this->giveLinearElasticMaterial() );
int numberOfActiveCracks = status->giveNumberOfTempActiveCracks();
int i, j, indi, indj, ii, jj;
double G, princStressDis, princStrainDis;
FloatMatrix de, invDe, compliance, dcr, d, df, t, tt, tempCrackDirs;
FloatArray principalStressVector, principalStrainVector;
IntArray mask;
if ( ( rMode == ElasticStiffness ) || ( numberOfActiveCracks == 0 ) ) {
lMat->giveCharacteristicMatrix(answer, form, rMode, gp, atTime);
return;
}
// this->updateActiveCrackMap(gp) must be done after restart.
this->updateActiveCrackMap(gp);
status->giveTempCrackDirs(tempCrackDirs);
this->giveNormalElasticStiffnessMatrix(de, ReducedForm, rMode, gp, atTime,
tempCrackDirs);
invDe.beInverseOf(de);
this->giveCrackedStiffnessMatrix(dcr, rMode, gp, atTime);
this->giveStressStrainMask( mask, ReducedForm, gp->giveMaterialMode() );
compliance.resize( mask.giveSize(), mask.giveSize() );
// we will set
// first we set compliances for normal streses in
// local coordinate system defined by crackplane
for ( i = 1; i <= 3; i++ ) {
if ( ( indi = this->giveStressStrainComponentIndOf(FullForm, gp->giveMaterialMode(), i) ) ) {
for ( j = 1; j <= 3; j++ ) {
if ( ( indj = this->giveStressStrainComponentIndOf(FullForm, gp->giveMaterialMode(), j) ) ) {
compliance.at(indi, indj) += invDe.at(i, j);
}
}
if ( status->isCrackActive(i) ) {
if ( dcr.at(i, i) <= 1.e-8 ) {
compliance.at(indi, indi) *= rcm2_BIGNUMBER;
} else {
compliance.at(indi, indi) += 1. / dcr.at(i, i);
}
}
}
}
status->getPrincipalStressVector(principalStressVector);
status->getPrincipalStrainVector(principalStrainVector);
// now remain to set shears
G = this->give(pscm_G, gp);
for ( i = 4; i <= 6; i++ ) {
if ( ( indi = this->giveStressStrainComponentIndOf(FullForm, gp->giveMaterialMode(), i) ) ) {
if ( i == 4 ) {
ii = 2;
jj = 3;
} else if ( i == 5 ) {
ii = 1;
jj = 3;
} else {
ii = 1;
jj = 2;
}
princStressDis = principalStressVector.at(ii) -
principalStressVector.at(jj);
princStrainDis = principalStrainVector.at(ii) -
principalStrainVector.at(jj);
if ( fabs(princStrainDis) < rcm_SMALL_STRAIN ) {
compliance.at(indi, indi) = 1. / G;
} else if ( fabs(princStressDis) < 1.e-8 ) {
compliance.at(indi, indi) = rcm2_BIGNUMBER;
} else {
compliance.at(indi, indi) = 2 * princStrainDis / princStressDis;
}
}
}
// now we invert compliance to get stiffness in reduced space
d.beInverseOf(compliance);
// delete compliance;
//
// now let d to grow to Full Format
//
this->giveStressStrainMask( mask, ReducedForm, gp->giveMaterialMode() );
df.beSubMatrixOfSizeOf(d, mask, 6);
//
// final step - transform stiffnes to global c.s
//
this->giveStressVectorTranformationMtrx(t, tempCrackDirs, 1);
tt.beTranspositionOf(t);
df.rotatedWith(tt);
if ( form == FullForm ) {
answer = df;
} else { // reduced form asked
this->giveStressStrainMask( mask, FullForm, gp->giveMaterialMode() );
answer.beSubMatrixOf(df, mask);
}
}
void
RCM2Material :: giveRealPrincipalStressVector3d(FloatArray &answer, GaussPoint *gp,
FloatArray &principalStrain,
FloatMatrix &tempCrackDirs,
TimeStep *atTime)
//
// returns real principal stress vector in 3d stress space of receiver according to
// previous level of stress and current
// strain increment, the only way, how to correctly update gp records
// updates principal strain and stress of the receiver's status.
//
{
int i, iter, ind;
double maxErr;
FloatArray crackStrainVector, reducedTotalStrainVector;
FloatArray strainIncrement, crackStrainIterativeIncrement;
FloatArray prevPrincipalStrain;
FloatArray dSigma;
FloatArray elastStrain, sigmaEl, sigmaCr(3);
FloatArray fullDSigma;
IntArray activatedCracks, crackMapping;
FloatMatrix dcr, de, decr, fullDecr, crackDirs;
RCM2MaterialStatus *status = ( RCM2MaterialStatus * ) this->giveStatus(gp);
/*
* if (status -> giveStressVector() == NULL) status->letStressVectorBe(new FloatArray(this->giveSizeOfReducedStressStrainVector(gp->giveMaterialMode())));
* if (status -> giveStrainVector() == NULL) status->letStrainVectorBe(new FloatArray(this->giveSizeOfReducedStressStrainVector(gp->giveMaterialMode())));
* // if (status -> givePlasticStrainVector() == NULL) status->letPlasticStrainVectorBe(new FloatArray(6));
* if (status -> giveStressIncrementVector() == NULL) status->letStressIncrementVectorBe(new FloatArray(this->giveSizeOfReducedStressStrainVector(gp->giveMaterialMode())));
* if (status -> giveStrainIncrementVector() == NULL) status->letStrainIncrementVectorBe(new FloatArray(this->giveSizeOfReducedStressStrainVector(gp->giveMaterialMode())));
* // if (status -> givePlasticStrainIncrementVector() == NULL) status->letPlasticStrainIncrementVectorBe(new FloatArray(6));
*/
/*
* // totalStressVector = gp -> giveStressVector()->GiveCopy();
* reducedTotalStrainVector = status -> giveStrainVector();
* reducedTotalStrainVector.add(fullStrainIncrement);
* crossSection->giveFullCharacteristicVector(totalStrainVector, gp, reducedTotalStrainVector);
* //delete reducedTotalStrainVector;
* // plasticStrainVector = status -> givePlasticStrainVector()->GiveCopy();
*
*
* // already cracked - next directions are determined
* // according to principal strain directions
* status->giveTempCrackDirs(tempCrackDirs);
* this->computePrincipalValDir (principalStrain, tempCrackDirs,
* totalStrainVector,
* principal_strain);
* status->letTempCrackDirsBe (tempCrackDirs);
*/
status->giveCrackStrainVector(crackStrainVector); // local one
status->giveCrackDirs(crackDirs);
if ( principalStrain.containsOnlyZeroes() ) {
// keep old principal values
status->letTempCrackDirsBe(crackDirs);
} else {
this->sortPrincDirAndValCloseTo(& principalStrain,
& tempCrackDirs, & crackDirs);
status->letTempCrackDirsBe(tempCrackDirs);
}
// compute de in local system
// for iso materials no transformation if stiffness required
//
// local strain increment
status->givePrevPrincStrainVector(prevPrincipalStrain);
strainIncrement.beDifferenceOf(principalStrain, prevPrincipalStrain);
status->letPrincipalStrainVectorBe(principalStrain);
this->giveNormalElasticStiffnessMatrix(de, FullForm, TangentStiffness,
gp, atTime, tempCrackDirs);
//
// construct mapping matrix of active cracks
// this mapping will dynamically change as
// some crack can unlo or reload
//
this->updateActiveCrackMap(gp);
status->giveCrackMap(crackMapping);
// start iteration until stress computed from elastic increment
// is equal to stress computed from cracking strain increment
// we do this computation in reduced stress strain space
dSigma.resize(0);
for ( iter = 1; iter <= 20; iter++ ) {
//
// first check if already cracked
//
if ( status->giveNumberOfTempActiveCracks() ) {
// active crack exist
this->giveCrackedStiffnessMatrix(dcr, TangentStiffness, gp, atTime);
fullDecr = de;
fullDecr.add(dcr);
decr.beSubMatrixOf(fullDecr, crackMapping);
if ( dSigma.giveSize() == 0 ) {
fullDSigma.beProductOf(de, strainIncrement);
dSigma.beSubArrayOf(fullDSigma, crackMapping);
}
decr.solveForRhs(dSigma, crackStrainIterativeIncrement);
for ( i = 1; i <= 3; i++ ) {
if ( ( ind = crackMapping.at(i) ) ) {
crackStrainVector.at(i) += crackStrainIterativeIncrement.at(ind);
}
}
// check for crack closing, updates also cracking map
this->checkIfClosedCracks(gp, crackStrainVector, crackMapping);
// elastic strain component
elastStrain.beDifferenceOf(principalStrain, crackStrainVector);
sigmaEl.beProductOf(de, elastStrain);
// Stress in cracks
for ( i = 1; i <= 3; i++ ) {
if ( crackMapping.at(i) ) {
sigmaCr.at(i) = giveNormalCrackingStress(gp, crackStrainVector.at(i), i);
}
}
// update status
status->letCrackStrainVectorBe(crackStrainVector);
} else {
//
// no active crack exist - elastic behaviour
//
elastStrain.beDifferenceOf(principalStrain, crackStrainVector);
sigmaEl.beProductOf(de, elastStrain);
sigmaCr.zero();
}
// check for new cracks
// and update crack map if necessary
// when we update map, we need to add new crack at end
// because sigmaCr is build
this->checkForNewActiveCracks(activatedCracks, gp, crackStrainVector,
sigmaEl, sigmaCr, principalStrain);
if ( activatedCracks.giveSize() ) {
// update crack map also
this->updateActiveCrackMap(gp, & activatedCracks);
status->giveCrackMap(crackMapping); // update crackMap
}
//
// compute unbalanced stress
// dSigma = sigmaEl - sigmaCr for active cracks
fullDSigma = sigmaEl;
fullDSigma.subtract(sigmaCr);
dSigma.beSubArrayOf(fullDSigma, crackMapping);
// find max error in dSigma
// if max err < allovedErr -> stop iteration
// allowed Err is computed relative to Ft;
// check only for active cracks
maxErr = 0.;
for ( i = 1; i <= dSigma.giveSize(); i++ ) {
if ( fabs( dSigma.at(i) ) > maxErr ) {
maxErr = fabs( dSigma.at(i) );
}
}
if ( maxErr < rcm_STRESSRELERROR * this->give(pscm_Ft, gp) ) {
status->letPrincipalStressVectorBe(sigmaEl);
answer = sigmaEl;
return;
}
} // loop
// convergence not reached
_error("GiveRealStressVector3d - convergence not reached");
}