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.