Interaction between an edge dislocation and a circular inhomogeneity with a mixed-type imperfect interface

We present an analytical solution (in series form) to the plane strain problem associated with an edge dislocation in the vicinity of a circular elastic inhomogeneity with a 'mixed-type imperfect interface.' The latter is a representation of the interfacial region in which the inhomogeneity and the matrix are endowed with separate and distinct Gurtin-Murdoch surface elasticities and bonded together through a spring-type imperfect interface. The coefficients in the resulting series solution are determined in a rather elegant manner requiring only the inverse of a number of 44 real symmetric positive definite matrices. The stress distribution in the composite structure and the normalized image force acting on the edge dislocation are found to be dependent on six size-dependent dimensionless parameters, among which four arise from the associated surface elasticities and two from the linear spring model of the interface. Asymptotic expressions for the image force when the dislocation is located at a remote distance from the inhomogeneity are also obtained analytically. The correctness of the solution is verified both numerically and analytically by comparison with existing results in the literature. Most importantly, our numerical results indicate that it is possible to find multiple equilibrium positions for the edge dislocation.