Convergence Analysis of a Local Stationarity Scheme for Rate-Independent Systems and Application to Damage

TL;DR

This paper analyzes a local stationarity scheme for approximating solutions to rate-independent systems with non-smooth dissipation and non-convex energy, proving existence of parametrized solutions and applying it to damage evolution.

Contribution

It introduces a convergence analysis for a local stationarity scheme in rate-independent systems, extending applicability to non-convex energies and damage models.

Findings

Accumulation points are parametrized solutions under Mosco-convergence.

The scheme guarantees existence of solutions in general settings.

Application to damage evolution demonstrates practical relevance.

Abstract

This paper is concerned with an approximation scheme for rate-independent systems governed by a non-smooth dissipation and a possibly non-convex energy functional. The scheme is based on the local minimization scheme introduced in [EM06], but relies on local stationarity of the underlying minimization problem. Under the assumption of Mosco-convergence for the dissipation functional, we show that accumulation points exist and are so-called parametrized solutions of the rate-independent system. In particular, this guarantees the existence of parametrized solutions for a rather general setting. Afterwards, we apply the scheme to a model for the evolution of damage.