Finite anti-plane shear of an infinite slab with a traction-free elliptical cavity: Bounds on the stress concentration factor

This paper provides an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous, isotropic, incompressible materials. The problem of an infinite slab with traction-free elliptical cavity subject to a state of finite simple shear deformation is considered. Explicit estimates are obtained for the maximum shear stress in terms of the cavity geometry, applied stress at infinity and constitutive parameters. The analysis is based on application of maximum principles for second-order quasilinear uniformly elliptic equations.