Stress concentration factors in finite anti-plane shear: numerical calculations and analytical estimates

In two recent papers [1, 2], an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous isotropic incompressible materials was presented. For the problem of an infinite slab, with a traction-free circular or elliptical cavity, subject to a state of finite simple shear deformation, explicit estimates for the stress concentration factor were obtained in terms of the cavity geometry, applied stress at infinity and constitutive parameters. In this paper, numerical results for these stress concentration factors are obtained using a finite-difference scheme and the analytical and numerical results are compared.