On the superlinear convergence in computational elasto-plasticity

We consider the convergence properties of return algorithms for a large class of rate-independent plasticity models. Based on recent results for semismooth functions, we can analyze these algorithms in the context of semismooth Newton methods guaranteeing local superlinear convergence. This recovers results for classical models but also extends to general hardening laws, multi-yield plasticity, and to several non-associated models. The superlinear convergence is also numerically shown for a large-scale parallel simulation of Drucker–Prager elasto-plasticity and an example for the modified Cam-clay model.

► We prove superlinear convergence for return algorithms in computational plasticity.
► The analysis is based on recent results for semismooth functions.
► It applies to general hardening laws, multi-yield plasticity, and to several non-associated models.
► It is also numerically shown for the Drucker–Prager and the modified Cam-clay model.