Stress Field Caused by Polygonal Inclusion

Abstract

In this paper, we analyze the elastic field caused by an arbitrary polygonal inclusion (with uniform eigenstrain prescribed) in an infinite elastic solid. Closed-form solutions are obtained using Green’s function technique. Numerical calculations are performed for the strain and stress distributions in and around a regular polygonal inclusion. It is shown that logarithmic-type stress singularity at each corner of the inclusion may vanish only for a square inclusion of a specific orientation. Unique properties of the Eshelby tensor of a regular polygonal inclusion found by Nozaki and Taya [ASME J. Appl. Mech., Vol. 64, 1997, pp. 495-502] are also investigated in detail and the terms that cause the properties are specified.