A circular inclusion with imperfect interface in finite plane elastostatics

Abstract

We consider a circular elastic inclusion embedded in a particular class of harmonic materials subjected to remote uniform stresses. The imperfect interface can be rate dependent as well as rate independent. First, we study the situation in which both rate-depending slip and diffusional relaxation are present on the sharp inclusion-matrix imperfect interface. It is found that in general, the internal Piola stresses within the inclusion are spatially non-uniform and decay with two relaxation times. Interestingly, the average mean Piola stress within the circular inclusion is time independent. Some extreme cases for the imperfect interface are discussed in detail. Particularly, we find a simple condition leading to internal uniform Piola stresses that decay only with a single relaxation time. Second, we investigate a rate-independent spring-type imperfect interface on which normal and shear tractions are proportional to the corresponding displacement jumps. It is found that in general, the internal Piola stresses are intrinsically non-uniform. A special kind of the spring-type interface leading to internal uniform Piola stresses is also found.