On a Circular Inclusion Embedded in an Infinite Matrix Subjected to a Point Load

Abstract

In this paper, an analytical solution for the two-dimensional mixed bound ary value problem of a circular inclusion is presented. The inclusion is embedded in an infinite medium and is subjected to a point force acting at the center of the inclusion. The inclusion/matrix interface is considered to be imperfect, across which the displacements may be discontinuous while the tractions remain continuous, as opposed to a perfectly bonded or smooth interface. The imperfect interface is modeled by a distribution of elastic springs, which transfer pressure directly but offer resistance to local extension and shear. For such an imperfect interface model, the basic principles of continuum mechanics re quire that the normal displacements be continuous at portions of the inclusion/matrix in terface where the corresponding normal tractions are compressive, so that no material penetration will occur. A dual series formulation is used in the present problem, and it leads to a weakly singular integral equation. The integral equation is solved numerically to obtain the stress distributions along the interface region.