Computational Methods for Elastoplasticity: An Overview of Conventional and Less-Conventional Approaches

The need of accurately reproducing the behaviour of elastoplastic materials in computational environments for the solution of engineering problems motivates the development of efficient and robust numerical schemes. These engineering problems often involve complex designs and/or conditions and are further complicated by the necessity of employing highly nonlinear and nonsmooth elastoplastic constitutive equations and constraints to describe material behaviour. Therefore, the numerical solution of such problems is not trivial and requires careful analyses to guarantee algorithm robustness, accuracy, and convergence in a reasonable amount of time. The aim of the present paper is to provide the reader with both an analysis and discussion, helpful in choosing the suitable numerical scheme when considering the implementation of a plasticity model. After a brief overview of the fundamental concepts for classical plasticity theory, we revise the state-of-the-art of computational methods by discussing conventional and less-conventional algorithms, formulated in a unified setting to allow for a comparison. Several approaches are implemented and discussed in representative numerical simulations.