A General Treatment of the Elastic Field of an Elliptical Inhomogeneity Under Antiplane Shear

Abstract

A general solution to the antiplane problem of an elliptical inhomogeneity in an isotropic elastic medium is provided. The proposed analysis is based upon the use of conformal mapping and Laurent series expansion of the corresponding complex potentials. The general expressions of the complex potentials are derived explicitly in both the elliptical inhomogeneity and the surrounding matrix. Several specific solutions are provided in closed form which are verified by comparison with existing ones. The effect of material and geometrical parameters upon the change of the elastic energy, due to the presence of an elliptical inhomogeneity, has also been considered.