STRESS-ANALYSIS OF HOLES IN ANISOTROPIC ELASTIC SOLIDS - CONFORMAL MAPPING AND BOUNDARY PERTURBATION

Complex-variable representations in the Stroh formalism are used to analyse a number of problems involving holes (voids) in a stressed anisotropic solid. One novel feature of our study is to consider morphological perturbations along the hole boundary. It is shown that the problem of a hole subjected to an applied stress field or an arbitrary boundary perturbation is equivalent to one with some prescribed traction along the hole surface. The boundary-perturbation analysis may be used in conjunction with a conformal-mapping scheme for elliptical hole shapes to study more complicated geometries. First-order perturbation solutions are given explicitly for smooth polygonal holes that are viewed as being perturbed from a reference circular hole. The perturbation solutions are used to estimate stress concentrations near a perturbed hole boundary, and to examine the morphological stability of a circular void in a stressed isotropic solid; in the latter study a bifurcation in the void shape, from a circle to less symmetrical geometries, is found to occur when either the stress level or the hole size reaches a critical value.