A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is characterized by an energy displaying both elastic and surface terms, and allows for a unified treatment of a wide range of settings, from epitaxially-strained thin films to crystalline cavities, and from capillarity problems to fracture models. The existence of minimizing configurations is established by adopting the direct method of the Calculus of Variations. The compactness of energy-equibounded sequences and energy lower semicontinuity are shown with respect to a proper selected topology in a class of admissible configurations that extends the classes previously considered in the literature. In particular, graph-like constraints previously considered for the setting of thin films and crystalline cavities are substituted by the more general assumption that the free crystalline interface is the boundary, consisting of an at most fixed finite number m of connected components, of sets of finite perimeter. Finally, it is shown that, as $$m\rightarrow \infty $$ m → ∞ , the energy of minimal admissible configurations tends to the minimum energy in the general class of configurations without the bound on the number of connected components for the free interface.

中文翻译：

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应力驱动重排不稳定性的统一模型

介绍了一种同时处理应力驱动重排不稳定性的变分模型，例如边界不连续性、内部裂纹、外部细丝、边缘分层、润湿和脆性断裂。该模型的特点是能量同时显示弹性和表面项，并允许对各种设置进行统一处理，从外延应变薄膜到结晶腔，从毛细管问题到断裂模型。最小化构型的存在性是通过采用变分法的直接方法来建立的。相对于一类可允许的配置中的适当所选择的拓扑结构示出了能量均越次序列和能量下半连续性的紧凑性，该概述拓扑结构延伸了先前在文献中考虑的类。特别是，先前为设置薄膜和结晶腔而考虑的类似图形的约束被更一般的假设所取代，即自由结晶界面是边界，由最多固定的有限数量 m 的连接分量和有限周长的集合组成。最后表明，当 $$m\rightarrow \infty $$m → ∞ 时，最小可容许构型的能量趋向于一般构型中的最小能量，而不受自由连通分量数的限制。界面。