Soft-solid deformation mechanics at the tip of an embedded needle

Motivated by a recently developed technique for measuring soft materials properties at the tip of an embedded needle [Zimberlin, et al., Soft Matter, 2007, 3, 763], the mechanics of elasticity- and surface tension-governed void growth within a neo-Hookean material is explored. Previous efforts to describe this technique relied on a hybrid spherical void/spherical cap approximation, thus assuming a spatially homogeneous deformation, i.e., no stress concentrations. We find that despite the inhomogeneities in needle-mediated growth, utilization of an areal surface stretch ratio as the deformation parameter yields good agreement between the spherical void and needle geometries.