Interaction between an edge dislocation and a circular elastic inhomogeneity with Steigmann-Ogden interface

We propose an effective method for the solution of the plane problem of an edge dislocation in the vicinity of a circular inhomogeneity with Steigmann-Ogden interface. Using analytic continuation, the pair of analytic functions defined in the infinite matrix surrounding the inhomogeneity can be expressed in terms of the pair of analytic functions defined inside the circular inhomogeneity. Once the two analytic functions defined in the circular inhomogeneity are expanded in Taylor series with unknown complex coefficients, the Steigmann-Ogden interface condition can be written explicitly in complex form. Consequently, all of the complex coefficients appearing in the Taylor series can be uniquely determined so that the two pairs of analytic functions are then completely determined. An explicit and general expression of the image force acting on the edge dislocation is derived using the Peach-Koehler formula.

Automated summary

In this paper, an effective method is proposed for solving the plane problem of an edge dislocation near a circular inhomogeneity with Steigmann-Ogden interface. By using analytic continuation, the pair of analytic functions defined in the infinite matrix surrounding the inhomogeneity can be expressed in terms of the pair of analytic functions defined inside the circular inhomogeneity. The Steigmann-Ogden interface condition can be explicitly written in complex form by expanding the two analytic functions defined inside the circular inhomogeneity in Taylor series with unknown complex coefficients. The image force acting on the edge dislocation is derived using the Peach-Koehler formula.