void
TensorMechanicsPlasticWeakPlaneShear::activeConstraints(const std::vector<Real> & f, const RankTwoTensor & stress, const Real & intnl, const RankFourTensor & Eijkl, std::vector<bool> & act, RankTwoTensor & returned_stress) const
{
act.assign(1, false);
returned_stress = stress;
if (f[0] <= _f_tol)
return;
// in the following i will derive returned_stress for the case smoother=0
Real tanpsi = tan_psi(intnl);
Real tanphi = tan_phi(intnl);
// norm is the normal to the yield surface
// with f having psi (dilation angle) instead of phi:
// norm(0) = df/dsig(2,0) = df/dsig(0,2)
// norm(1) = df/dsig(2,1) = df/dsig(1,2)
// norm(2) = df/dsig(2,2)
std::vector<Real> norm(3, 0.0);
Real tau = std::sqrt(std::pow((stress(0,2) + stress(2,0))/2, 2) + std::pow((stress(1,2) + stress(2,1))/2, 2));
if (tau > 0.0)
{
norm[0] = 0.25*(stress(0, 2)+stress(2,0))/tau;
norm[1] = 0.25*(stress(1, 2)+stress(2,1))/tau;
}
else
{
returned_stress(2, 2) = cohesion(intnl)/tanphi;
act[0] = true;
return;
}
norm[2] = tanpsi;
// to get the flow directions, we have to multiply norm by Eijkl.
// I assume that E(0,2,0,2) = E(1,2,1,2), and E(2,2,0,2) = 0 = E(0,2,1,2), etc
// with the usual symmetry. This makes finding the returned_stress
// much easier.
// returned_stress = stress - alpha*n
// where alpha is chosen so that f = 0
Real alpha = f[0]/(Eijkl(0,2,0,2) + Eijkl(2,2,2,2)*tanpsi*tanphi);
if (1 - alpha*Eijkl(0,2,0,2)/tau >= 0)
{
// returning to the "surface" of the cone
returned_stress(2, 2) = stress(2, 2) - alpha*Eijkl(2, 2, 2, 2)*norm[2];
returned_stress(0, 2) = returned_stress(2, 0) = stress(0, 2) - alpha*2*Eijkl(0, 2, 0, 2)*norm[0];
returned_stress(1, 2) = returned_stress(2, 1) = stress(1, 2) - alpha*2*Eijkl(1, 2, 1, 2)*norm[1];
}
else
{
// returning to the "tip" of the cone
returned_stress(2, 2) = cohesion(intnl)/tanphi;
returned_stress(0, 2) = returned_stress(2, 0) = returned_stress(1, 2) = returned_stress(2, 1) = 0;
}
returned_stress(0, 0) = stress(0, 0) - Eijkl(0, 0, 2, 2)*(stress(2, 2) - returned_stress(2, 2))/Eijkl(2, 2, 2, 2);
returned_stress(1, 1) = stress(1, 1) - Eijkl(1, 1, 2, 2)*(stress(2, 2) - returned_stress(2, 2))/Eijkl(2, 2, 2, 2);
act[0] = true;
}
RankTwoTensor
TensorMechanicsPlasticWeakPlaneShear::flowPotential(const RankTwoTensor & stress, const Real & intnl) const
{
return df_dsig(stress, tan_psi(intnl));
}