Disturbed elastic fields in a circular 2D finite domain containing a circular inhomogeneity and a finite interfacial zone

Abstract

In order to take into account the effect of a finite interfacial zone between the inhomogeneity and matrix in an inhomogeneous representative volume element (RVE), analytical solutions for a 3-phase inclusion problem are needed. In this study, the primary focus is placed on a 3-phase concentric configuration for a 2D RVE, for which the exterior matrix is bounded and different elastic properties are assigned to the interior inclusion, interfacial zone and exterior matrix. In addition to the inhomogeneity induced by material mismatch, arbitrary uniform eigenstrains are allowed to occur independently within the interfacial zone and inclusion, respectively. In this study, the analytical solution is pursued via the complex potential method with the aid of 2 auxiliary potential functions. Based on the Sokhotski-Plemelj theorem, the complex potentials in each phase are constructed to account for the eigenstrains existing in the inclusion and the interfacial zone, as well as the imposed boundary conditions on the exterior matrix. The identification of the coefficients in the complex potential functions gives the analytical expressions for the disturbance induced by the inhomogeneity and eigenstrains. When compared with FEM simulations, a firm agreement is achieved for 3-phase concentric 2D finite domains. Furthermore, if the exterior matrix is extended to infinity, the obtained analytical solution reproduces the results given by Luo and Weng for uniform eigenstrain within the inclusion and by Markenscoff and Dundurs for uniform eigenstrain in the interfacial zone.