Crystal Plasticity Material Implementation: Slow convergence

[kismatpandey]

I've implemented a crystal plasticity material model in 4C and compared it with the same implementation in PRISMS (deal.ii based). The final displacement fields match exactly to 6 decimal places, but the nonlinear convergence behavior is dramatically different.

Final time step:
PRISMS(deal.ii): 3 Newton iterations (quadratic convergence)
4C: 19 Newton iterations (linear convergence)

Tangent matrices at quad points are numerically identical between codes.

My implementation calculates dP/dF (material tangent) and returns it via the cmat parameter in the evaluate function:
void evaluate(..., Core::LinAlg::SymmetricTensor<double, 3, 3, 3, 3>& cmat, ...)

I think the slow convergence has to do the tangent stiffness. I am 100% sure that the tangent stiffness calculation is correct.

My question is:
What format does 4C expect for the material tangent?

Options I'm considering:

1. dP/dF (what I currently provide)
2. (dP/dF)^T (transpose)
3. Spatial tangent instead of material tangent
4. Specific Voigt ordering

The identical final results suggest correct physics, but poor Newton convergence indicates wrong tangent format.
Any guidance appreciated! Thank you

[amgebauer]

Hi @kismatpandey,

In our solid constitutive models, 4C expects the derivative dS/dE (derivative of the 2PK stress w.r.t. Green-Lagrange strain). If you provide dP/dF, this is probably the cause of the bad Newton convergence. If you use symmetric tensors consitently, you don't have to bother with any internal Voigt-ordering. I recommend you to use these (and not the legacy Core::LinAlg::Matrix).

[kismatpandey]

@amgebauer Thank you! It was indeed the issue. Now that I converted dP_dF into dS_dE, it converges well!