A general solution for plane problem of anisotropic media containing elliptic inhomogeneity with polynomial eigenstrains

•Problem of anisotropic elliptic inhomogeneities in an infinite anisotropic medium.•To illustrate distributions of stresses and displacements.•Induced symmetric distributions of stress and deformation by symmetric eigenstrains.•Induced asymmetric distributions of stress and deformation by uniform eigenstrains.

A general complex function method is proposed to solve the plane problem for a single anisotropic elliptic inhomogeneity embedded in an infinite anisotropic medium. The system is subjected to polynomial eigenstrains as well as far-field stresses. A general procedure based on Laurent series is presented using continuous conditions at the interface. Numerical examples are given and distribution of stresses and displacements at the interface e are analyzed for prescribed polynomial eigenstrains of degrees 0, 1 and 2. Effect of inclined angle of principal axes for anisotropic material on translation and rotation of the inhomogeneity is also illustrated. For a circular inhomogeneity, its anisotropy may cause asymmetrical deformation under uniform eigenstrains.