Stress concentration and surface instability of anisotropic solids with slightly wavy boundary

This paper presents a first order perturbation analysis of stress concentration and surface morphology instability of elastically anisotropic solids. The boundary of the solids under consideration is periodic along two orthogonal directions. The magnitude of the undulation is sufficiently small so that a half-space model can be used for simplification. We derive expressions for the stress concentration factors and the critical wavelength of the perturbation in terms of the remote stresses, surface energy anisotropy and the elastic anisotropy of the solid. Numerical applications to cubic materials using Barnett–Lothe integrals are also given.