Size-dependent interaction between a screw dislocation and an inhomogeneity of arbitrary shape in an applied stress field

We present a general approximate solution for a screw dislocation interacting with an inhomogeneity of arbitrary shape in an applied stress field. The analysis is based on the Eshelby inhomogeneity theory. As special cases, explicit solutions for some common inhomogeneity shapes are obtained, from which size-dependent effects of dislocation stress field and the applied stress field on the interaction can be identified.     

On convergence of the generalized Maxwell scheme: conductivity of composites containing cubic arrays of spherical particles

The Maxwell concept of equivalent inhomogeneity generalized to account for the interactions between the particles in the cluster and combined with recently reported results on the polarizability of a cube is used to evaluate the effective conductivities of the materials reinforced by cubic arrays of spherical particles. New numerical results demonstrate that the estimates of the effective properties based on the generalized Maxwell scheme with the equivalent inhomogeneity of cubic shape converge to the accurate periodic benchmark solutions, unlike spherical shape-based estimates.