Analytical solution of elastic fields induced by a 2D inclusion of arbitrary polygonal shape

Abstract

We generalize a recent application of the equivalent inclusion method, Jin et al. (2011), to derive the elastic field induced by a constant eigenstrain applied to an elliptic inclusion whose boundary is approximated by a polygon, the number of sides being assigned so as to recover the analytical values of the entries of the Eshelby tensor. The generalization consists in the fact that displacements, strains, stresses and the Eshelby tensor can be given a unique expression, holding inside and outside the inclusion, thus avoiding the recourse to the derivation of distinct expressions, based upon different approaches, for the elastic fields. The proposed approach has been successfully applied to evaluate the elastic fields induced by an elliptical cavity in a linear isotropic infinite plate subjected to a remote loading by recovering the classical solutions by Inglis (1913) and Maugis (1992). Furthermore it can easily be applied to elliptical holes arbitrarily oriented with respect to the loading direction.