hp-Finite Elements for Elastoplasticity
For researchers in computational mechanics, this work offers a novel numerical method for elastoplasticity problems, but the results are theoretical without concrete numerical improvements.
This paper develops hp-finite element discretizations for elastoplasticity with linear kinematic hardening, introducing a mixed variational formulation to handle non-differentiability and enabling an efficient semismooth Newton solver. Error analysis is provided.
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.