#### Vol. 15, No. 4, 2020

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Closed-form solutions for an edge dislocation interacting with a parabolic or elliptical elastic inhomogeneity having the same shear modulus as the matrix

### Xu Wang and Peter Schiavone

Vol. 15 (2020), No. 4, 539–554
##### Abstract

We use complex variable methods to derive closed-form solutions to the problems of an edge dislocation interacting with a parabolic or elliptical elastic inhomogeneity embedded inside an infinite elastic matrix. The inhomogeneity and the matrix have the same shear modulus but distinct Poisson’s ratios. The edge dislocation can be located in the matrix, in the elastic inhomogeneity or precisely on the parabolic or elliptical interface. Explicit expressions of the image force acting on the edge dislocation as a result of its interaction with the parabolic or elliptical elastic inhomogeneity are presented. Our analyses indicate that the image force on an edge dislocation inside a parabolic or an elliptical elastic inhomogeneity is invariant with the direction of the Burgers vector of the edge dislocation.

##### Keywords
parabolic elastic inhomogeneity, elliptical elastic inhomogeneity, edge dislocation, image force, closed-form solution