An Eshelby inclusion of parabolic shape in an anisotropic elastic plane

Abstract

An analytical solution is derived to the Eshelby's problem of a parabolic inclusion undergoing uniform in-plane and anti-plane eigenstrains in an anisotropic elastic plane. The stresses, total strains and rigid-body rotation are found to be uniform inside the parabolic inclusion. In addition, we obtain real-form expressions of these internal uniform physical quantities in terms of the reduced elastic compliances and the imposed eigenstrains. The constant Eshelby's tensor inside the parabolic inclusion can be completely determined by the reduced elastic compliances.