Interface Effect on the Dynamic Stress around an Elliptical Nano-Inhomogeneity Subjected to Anti-Plane Shear Waves

In the design of advanced micro- and nanosized materials and devices containing inclusions, the effects of surfaces/interfaces on the stress concentration become prominent. In this paper, based on the surface/interface elasticity theory, a two-dimensional problem of an elliptical nano-inhomogeneity under anti-plane shear waves is considered. The conformal mapping method is then applied to solve the formulated boundary value problem. The analytical solutions of displacement fields are expressed by employing wave function expansion method, the expanded mode coefficients are determined by satisfying the boundary conditions at the interfaces of the nano-inhomogeneity. Analyses show that the effect of the interfacial properties on the dynamic stress is significantly related to the wave frequency of incident waves, the shear modulus ratio of the nano-inhomogeneity and the matrix, and the dimensions of the elliptical nano-inhomogeneity. Comparison with the previous results is also presented.