On the existence of minimizers with prescribed singular points in nonlinear elasticity

Experiments on elastomers have shown that sufficiently large triaxial tensions induce the material to exhibit holes that were not previously evident. In this paper, conditions are presented that allow one to use the direct method of the calculus of variations to deduce the existence of hole creating deformations that are global minimizers of a nonlinear, purely elastic energy. The crucial physical assumption used is that there are a finite (possibly large) number of material points in the undeformed body that constitute the only points at which cavities can form. Each such point may be viewed as a preexisting flaw or an infinitesimal microvoid in the material.