Anti-plane Problem Of An Elliptical Inhomogeneity In Anisotropic Media With A Single Plane Of Symmetry

The most general degree of anisotropy characterizing elastic materials is anisotropy with a single plane of symmetry except the complete anisotropy. This thesis presents the analytical solution for anti-plane problem of an elliptical inhomogeneity with non-uniformly distributed eigenstains embedded in anisotropic elastic media with a single plane of symmetry. For the case that the eigenstrains is in the form of linear function of Cartesian coordinates of the points of the inhomogeneity, the solution for the stress and strain fields is analytically derived based on the polynomial conservation theorem, the complex function method and conformal transformation together with the principle of minimum strain energy. The induced elastic fields are verified by checking the continuity condition for the stress at the interface between the inhomogeneity and matrix. Especially, the present solution will reduce to the known result for some special cases. In addition, numerical examples are given and the distributions of stress and strain inside the inhomogeneity and at the interface are illustrated. Further, for the case of eigenstrains having the form of a quadratic polynomial function, some analytical expressions for the strain energy of the inhomogeneity/matrix system and stress at the interface of the ellipse are obtained, and these formulae can be used to determine finally the elastic field for the system.