Linearized plasticity is the evolutionary \Gamma-limit of finite plasticity

TL;DR

This paper rigorously justifies the classical linearization approach in plasticity by proving the convergence of finite-strain elastoplasticity solutions to linearized elastoplasticity solutions using b3-convergence in the small-deformations limit.

Contribution

It provides a rigorous mathematical proof that the linearized elastoplasticity model is the limit of the finite-strain model as deformations become small.

Findings

Finite-strain elastoplasticity solutions converge to linearized solutions

The convergence is established via b3-convergence for rate-independent processes

The result confirms the classical linearization approach in plasticity

Abstract

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.