  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.
