hp-Finite Elements for Elastoplasticity

TL;DR

This paper develops hp-finite element methods for elastoplasticity, introducing a mixed formulation to handle non-differentiability and enabling efficient nonlinear solving with error analysis.

Contribution

It presents a novel mixed variational formulation for elastoplasticity and discretization strategies that facilitate efficient semismooth Newton solutions.

Findings

Decoupled nonlinear system formulation enables efficient computation.

A priori and a posteriori error analyses are provided.

Mixed formulation effectively handles non-differentiability in plasticity models.

Abstract

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational formulation is introduced to resolve the non-differentiablility of the so-called plasticity functional appearing in the weak formulation of the model problem as a variational inequality of the second kind. The discretization of the mixed formulation is then represented as a system of decoupled nonlinear equations which allows the application of an efficient semismooth Newton solver. Finally, an a priori and a posteriori error analysis is given.