Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations

We propose an elegant and concise general method for the solution of a problem involving the interaction of a screw dislocation and a nano-sized, arbitrarily shaped, elastic inhomogeneity in which the contribution of interface/surface elasticity is incorporated using a version of the Gurtin–Murdoch model. The analytic function inside the arbitrarily shaped inhomogeneity is represented in the form of a Faber series. The real periodic function arising from the contribution of the surface mechanics is then expanded as a Fourier series. The resulting system of linear algebraic equations is solved through the use of simple matrix algebra. When the elastic inhomogeneity represents a hole, our solution method simplifies considerably. Furthermore, we undertake an analytical investigation of the challenging problem of a screw dislocation interacting with two closely spaced nano-sized holes of arbitrary shape in the presence of surface stresses. Our solutions quite clearly demonstrate that the induced elastic fields and image force acting on the dislocation are indeed size-dependent.