The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

Abstract

T he problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x t , then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x t .