One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

Abstract

We offer a finite-time stability result for Moreau sweeping processes on the plane withperiodically moving polyhedron. The result is used to establish the convergence of stress evolution of asimple network of elastoplastic to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the verticesof the polyhedron makes finite-time stability impossible.