率无关系统局部平稳格式的收敛性分析及其在损伤问题中的应用
Convergence Analysis of a Local Stationarity Scheme for Rate-Independent Systems and Application to Damage
摘要：
本文研究了一类具有非光滑耗散和可能非凸能量泛函的速率无关系统的近似格式。该方案基于[EM06]中介绍的局部最小化方案，但依赖于底层最小化问题的局部平稳性。在耗散泛函Mosco收敛的假设下，证明了该速率无关系统的聚集点的存在性，即所谓的参数化解。特别是，这保证了一个相当一般的设置参数化的解决方案的存在。之后，我们将该计划的损伤演化模型。
英文摘要：
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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