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.
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