const C2Vector OrthoProject (const CVector &vVec, int iAxis)
{
switch (iAxis)
{
case axisX:
return C2Vector(vVec.Y(), vVec.Z());
case axisY:
return C2Vector(vVec.X(), vVec.Z());
case axisZ:
return C2Vector(vVec.X(), vVec.Y());
default:
ASSERT(false);
return C2Vector();
}
}
// EVALUATE THE PLASTIC POTENTIAL DERIVATIVES
void BorjaCamClayExplicitFlowRule::CalculatePlasticPotentialDerivatives( const Vector& rStressVector, Vector& rFirstDerivative, Matrix & rSecondDerivative)
{
rFirstDerivative = ZeroVector(1);
rSecondDerivative = ZeroMatrix(1,1);
double M = mpYieldCriterion->GetHardeningLaw().GetProperties()[CRITICAL_STATE_LINE] ;
double Friction = mpYieldCriterion->GetHardeningLaw().GetProperties()[INTERNAL_FRICTION_ANGLE];
if ( fabs( Friction) > 1e-5)
return;
Vector StressV = rStressVector;
double MeanP = 0;
for (unsigned int i=0 ; i < 3; i++)
MeanP += StressV(i) / 3.0;
for (unsigned int i = 0; i < 3; i++)
StressV(i) -= MeanP;
// COMPUTE J2;
double J2InvSQ = 0;
for (unsigned int i = 0; i < 3; i++)
J2InvSQ += pow( StressV(i), 2.0);
for (unsigned int i = 0; i < 3; i++)
J2InvSQ += 2.0 * pow( StressV(i), 2.0);
J2InvSQ = sqrt( J2InvSQ/2.0);
if ( J2InvSQ < 1E-5)
return;
// J2 firstDeriv
Vector C2Vector = StressV;
for (unsigned int i = 3; i < 6; i++)
C2Vector(i) *= 2.0;
C2Vector /= 2.0* J2InvSQ;
// C2Matrix
Matrix C2Matrix = ZeroMatrix(6,6);
for (unsigned int i = 0; i < 6; i++) {
for (unsigned int j = 0; j < 6; j++) {
double times = 0.5;
if ( i > 2)
times *= 2.0;
if ( j > 2 )
times *= 2.0;
C2Matrix(i,j) -= times* StressV(i)*StressV(j) / pow( J2InvSQ, 2.0);
}
}
for (unsigned int i = 0; i < 3; i++) {
C2Matrix(i,i) += 1.0;
for (unsigned int j = 0; j < 3; j++) {
C2Matrix(i,j) -= 1.0/3.0;
}
}
for (unsigned int i = 3; i < 6; i++)
C2Matrix(i,i) += 2.0;
C2Matrix /= 2.0 * J2InvSQ;
rSecondDerivative = 6.0 / ( M*M) * J2InvSQ * C2Matrix;
Vector C1Der = ZeroVector(6);
for (unsigned int i = 0; i < 3; i++)
C1Der(i) = 1.0/3.0;
for (unsigned int i = 0; i < 6; i++) {
for (unsigned int j = 0; j < 6; j++) {
rSecondDerivative(i,j) += 6.0/ (M*M) * C2Vector(i)*C2Vector(j) + 2.0*C1Der(i)*C1Der(j);
}
}
}
