What algorithms could be the most possible approach for both the local integration of the constitutive model and the global iteration in the boundary value problem (say a footing case)?
Here I mean a highly non-linear work hardening-softening model for granular (cohesionless) material. Closest point projection method and cutting plane method in combination with a Newton-Raphson method both failed in my attempts to implement the model in ABAQUS Umat. Could anyone give me some advice?
Have you checked whether you have the right expression of the algorithmic tangent? If it is correct, you should be able to get quadratic convergence in general. In cases of softening behavior, some extra consideration is needed in the solution strategy to track the peak and softrning response, e.g. Arc length method, etc.
without much information, it is quite tough to identify what went wrong. Can you elaborate on why your current algorithm does not work?
Thank you for your answer. In ABAQUS, I only dealt with the local problem in its user subroutine. The local Jacobean was also given in the subroutine. The global iteration is Full-Newton method in this software. Using one element mesh, I can obtain a smooth stress-strain curve. However, if this one element was divided into many elements, the solution diverged immediately after the peak. Please have a check on the figures.
More severe case is the footing case. The elements suffer very low initial stress at the beginning of the simulation. Local non-convergence happened in all the elements, so the solution diverged immediately after start.
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