On the numerical implementation of the Closest Point Projection algorithm in anisotropic elasto-plasticity with nonlinear mixed hardening

Abstract

In finite element analysis, among the possible frameworks for stress-point integration algorithms in computational elastoplasticity, the implicit Closest Point Projection (CPP) algorithm is probably the most used one. The idea behind this algorithm is that all necessary variables, including the flow and hardening directions, are iteratively updated and enforced at the final solution. Therefore the algorithm is fully implicit and the final solution is independent of previous iterations. However, there are several possible implementations of the ideas behind the CPP algorithm. Even though asymptotic quadratic convergence may be obtained in all implementations if the algorithm is properly linearized, these different possibilities result in a different number of local iterations and in a different computational effort. Small stress-integration algorithms are frequently the only iterative core of large strain elastoplastic formulations. At the same time they are responsible for a large share of the overall computational time in finite element simulations and key in the overall robustness. In this work we present a new algorithm based on the ideas of the Closest Point Projection algorithm for anisotropic elastoplasticity with mixed hardening. We also compare our proposal with other possible implementations of the CPP algorithm for the same problem, namely the General CPP implementation and the Governing Parameter Method. We show that our proposal is in general more efficient.