In-plane deformations of a nano-sized circular inhomogeneity with interface slip and diffusion

Abstract

We consider time-dependent plane strain deformations of a nanosized circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to uniform remote stresses. The inhomogeneity and the matrix are each endowed with separate and distinct Gurtin–Murdoch surface elasticities. In addition, both rate-dependent slip and mass transport resulting from stress-driven diffusion occur concurrently on the inhomogeneity/matrix interface. A simple yet effective method is proposed to derive a closed-form solution. The stress distributions in the composite are size-dependent and evolve with two relaxation times. Explicit expressions for the relaxation times depend on four size-dependent parameters: two arising from interface slip and diffusion and two from surface elasticities. The stress field inside the inhomogeneity is spatially non-uniform and time-dependent when the remote loading is non-hydrostatic; conversely, it is uniform, hydrostatic and time-independent when the remote loading is hydrostatic.