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arXiv · 2104.14997

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

Michael Sievers
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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.

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Michael Sievers. 2021-04-30. Convergence Analysis of a Local Stationarity Scheme for Rate-Independent Systems and Application to Damage. https://arxiv.org/abs/2104.14997

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