  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.
  Existence of minimizing configurations is established by adopting the direct
method of the Calculus of Variations. 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 $m\to\infty$, 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.
