Concentrated Force Near a Smooth Circular Inclusion

Abstract

A concentrated force applied to an infinite matrix near a smooth circular inclusion is discussed. The smooth interface is defined as one that allows slip, but does not transmit shearing tractions. The solution is partially in terms of series, but for certain combinations of materials the series sum to elementary functions. The solution which is of significance for applications in micromechanics exhibits interesting behavior also from the point of view of classical elastostatics. When the force is allowed to approach the interface, the singularity for the force shows dependence on the curvature of the interface. In this respect the smooth interface between two materials in two dimensions resembles a curved boundary in three dimensions.