The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain

We consider the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains. The particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion. Eshelby showed that in such a situation the induced strain field within the inclusion is also characterized by a polynomial of the same order. However, the explicit expression for this polynomial seems to have not yet been reported in the literature. The present study fills this gap.