脱粘模型准静态演化的自由边界方法
A free boundary approach to the quasistatic evolution of debonding models
AI总结：
本文通过将脱粘过程转化为单相伯努利自由边界问题，利用函数空间中的极小化移动方案，在开集类中建立了基于全局极小值和能量平衡的准静态演化存在性。
摘要：
将粘合膜从基底上逐步脱粘的力学过程描述为集合的准静态变分演化，并在此进行研究。基于合适泛函的全局极小值以及能量平衡，在自然开集类中获得了能量解的存在性，改进并简化了文献中已有的结果。所提出的方法依赖于将该模型等价地重新表述为著名的单相伯努利自由边界问题。这一观点允许在函数空间而非更复杂的集合框架中执行极小化移动方案。然而，为了涵盖现象的不可逆性，在每个离散时间步跟踪脱粘区域仍然至关重要，从而实际上产生了一个耦合算法。
英文摘要：
The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a suitable functional together with an energy balance, is obtained within the natural class of open sets, improving and simplifying previous results known in literature. The proposed approach relies on an equivalent reformulation of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This point of view allows performing the Minimizing Movements scheme in spaces of functions instead of the more complicated framework of sets. Nevertheless, in order to encompass irreversibility of the phenomenon, it remains crucial to keep track of the debonded region at each discrete time-step, thus actually resulting in a coupled algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
