One-dimensional elastoplastic models with isotropic hardening as differential inclusions in primal form

Abstract

To improve the numerical simulation of rockfall protection barriers, this work addresses an extension of a one-dimensional model for elastoplasticity using a friction element and a spring in series, to include isotropic hardening and unilateral behavior. We reformulate the resulting system of differential inclusions in primal form and develop a timestepping scheme via an extended version of Moreau's midpoint rule. The scheme handles nonsmooth dynamics consistently, allowing to include frictional contact and impacts. The results provide a rigorous and implementable framework for simulating coupled elastoplastic frictional contact systems, contributing to the analysis and computation of nonsmooth rate-independent processes.