/** Multiplies tensor A, on the left by it's transpose, A^T to give A^T * A
And returns the answer in a symmetric tensor*/
void TensorArray_MultiplyByLeftTranspose(TensorArray tensor, Dimension_Index dim, SymmetricTensor result) {
TensorArray tensorTranspose;
TensorArray fullTensorResult;
TensorArray_Transpose( tensor, dim, tensorTranspose);
TensorArray_MultiplyByTensorArray( tensorTranspose, tensor, dim, fullTensorResult );
/** Answer is automatically a symmetric tensor by definition */
TensorArray_GetSymmetricPart( fullTensorResult, dim, result);
return;
}
void DruckerPrager_Extra_GetSlipVector(void* druckerPrager_Extra,
ConstitutiveMatrix* constitutiveMatrix,
MaterialPointsSwarm* materialPointsSwarm,
Element_LocalIndex lElement_I,
MaterialPoint* materialPoint,
Coord xi,
double dpFrictionCoefficient) {
DruckerPrager_Extra* self = (DruckerPrager_Extra*) druckerPrager_Extra;
DruckerPrager_Extra_Particle* particleExt;
double currentVelocityGradient[9];
Eigenvector eigenvectorList[3];
double strainRate_ns[2];
SymmetricTensor currentStrainRate;
XYZ normal[2];
XYZ slip[2];
double theta;
int favourablePlane, err;
Dimension_Index dim = constitutiveMatrix->dim;
/* stupid way to recover the integration point from the materialPoint
* * TODO: FIXCONSTITUTIVE use integration point only */
IntegrationPoint* integrationPoint = (IntegrationPoint*) Swarm_ParticleAt( constitutiveMatrix->integrationSwarm,
constitutiveMatrix->currentParticleIndex );
particleExt = (DruckerPrager_Extra_Particle*) ExtensionManager_Get( materialPointsSwarm->particleExtensionMgr, materialPoint, self->particleExtHandle );
/* get velocity Gradients */
err = PpcManager_Get( self->mgr, lElement_I, integrationPoint, self->velocityGradientsTag, currentVelocityGradient );
if( err ) assert(0);
TensorArray_GetSymmetricPart( currentVelocityGradient, dim, currentStrainRate );
/* Slip vector does not have anything to do with the constitutive behaviour since isotropic so should try and find max shear strain rate by calculating eigenvectors of strainrate */
SymmetricTensor_CalcAllEigenvectors( currentStrainRate, dim, eigenvectorList );
/* Since isotropic, the max shear stress always lies at theta = 45 degrees on mohr circle, so to for strain rate? */
theta = M_PI / 4.0;
if (dim == 2) {
/* Identify potential failure directions */
StGermain_RotateCoordinateAxis( slip[0], eigenvectorList[0].vector, K_AXIS, +theta);
StGermain_RotateCoordinateAxis( slip[1], eigenvectorList[0].vector, K_AXIS, -theta);
StGermain_RotateCoordinateAxis( normal[0], eigenvectorList[0].vector, K_AXIS, 0.5*M_PI + theta);
StGermain_RotateCoordinateAxis( normal[1], eigenvectorList[0].vector, K_AXIS, 0.5*M_PI - theta);
}
else {
/* Identify potential failure directions */
StGermain_RotateVector( slip[0], eigenvectorList[0].vector, eigenvectorList[1].vector, + theta );
StGermain_RotateVector( slip[1], eigenvectorList[0].vector, eigenvectorList[1].vector, - theta );
StGermain_RotateVector( normal[0], eigenvectorList[0].vector, eigenvectorList[1].vector, 0.5*M_PI + theta);
StGermain_RotateVector( normal[1], eigenvectorList[0].vector, eigenvectorList[1].vector, 0.5*M_PI - theta);
}
/* Resolve shear strain-rate for the potential failure planes */
strainRate_ns[0] = fabs(TensorArray_MultiplyByVectors( currentVelocityGradient, slip[0], normal[0], dim ));
strainRate_ns[1] = fabs(TensorArray_MultiplyByVectors( currentVelocityGradient, slip[1], normal[1], dim ));
/* Choose the plane which is oriented favorably for continued slip */
favourablePlane = (strainRate_ns[0] > strainRate_ns[1] ? 0 : 1);
memcpy( particleExt->slip, slip[favourablePlane], dim * sizeof(double) );
particleExt->slipRate = strainRate_ns[ favourablePlane ];
}
