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.

我们使用复杂的变量方法来导出闭合形式的解，以解决边缘错位与嵌入无限弹性矩阵内的抛物线或椭圆形弹性不均匀性相互作用的问题。不均匀性和基体具有相同的剪切模量，但具有不同的泊松比。边缘位错可以位于矩阵中，处于弹性不均匀性中，也可以位于抛物线或椭圆形界面上。给出了图像力由于其与抛物线或椭圆形弹性不均匀性相互作用而作用在边缘位错上的明确表达。我们的分析表明，在抛物线形或椭圆形弹性不均匀性内部的边缘位错上的像力随边缘位错的Burgers向量的方向不变。