Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.