The problem of the sudden growth and coalescence of voids in elastic media is considered. The Dirichlet energy is minimized among incompressible and invertible Sobolev deformations of a two-dimensional domain having $n$ microvoids of radius $\varepsilon$. The constraint is added that the cavities should reach at least certain minimum areas $v_{1},...,v_{n}$ after the deformation takes place. They can be thought of as the current areas of the cavities during a quasistatic loading, the variational problem being the way to determine the state to be attained by the elastic body in a subsequent time step. It is proved that if each $v_{i}$ is smaller than the area of a disk having a certain well defined radius, which is comparable to the distance, in the reference configuration, to either the boundary of the domain or the nearest cavity (whichever is closer), then there exists a range of external loads for which the cavities opened in the body are circular in the $\varepsilon \rightarrow 0$ limit.

中文翻译：

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非线性弹性固体中空隙聚结载荷的下限

考虑了弹性介质中空隙的突然增长和聚结的问题。Dirichlet 能量在二维域的不可压缩和可逆 Sobolev 变形中被最小化，该二维域具有半径为 $\varepsilon$ 的 $n$ 微空隙。添加了约束，即在变形发生后，空腔应至少达到某些最小面积 $v_{1},...,v_{n}$。它们可以被认为是准静态加载期间空腔的当前区域，变分问题是确定弹性体在随后的时间步长中要达到的状态的方法。证明如果每个 $v_{i}$ 小于具有某个明确定义的半径的圆盘的面积，这与距离相当，在参考配置中，