The equilibrium configurations of a one-dimensional variational model that
combines terms expressing the bulk energy of a deformable crystal and its
surface energy are studied. After elimination of the displacement, the
problem reduces to the minimization of a nonconvex and nonlocal functional of
a single function, the thickness. Depending on a parameter which strengthens
one of the terms comprising the energy at the expense of the other, it is
shown that this functional may have a stable absolute minimum or only a
minimizing sequence in which the term corresponding to the bulk energy is
forced to zero by the production of a crack in the material.