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An anisotropic elastic inhomogeneous elliptical inclusion

Xu Wang and Peter Schiavone

Vol. 17 (2022), No. 2, 181–192
Abstract

Using the Stroh sextic formalism, we study the problem of an anisotropic elastic inhomogeneous elliptical inclusion undergoing uniform eigenstrains embedded in an infinite anisotropic elastic matrix. The inhomogeneous inclusion and the matrix have separate elastic properties. A real-form solution of the internal uniform elastic field characterizing stresses, total strains and rigid-body rotation within the inhomogeneous elliptical inclusion is obtained in terms of the fundamental elasticity matrix for the elliptical inclusion and the Barnett–Lothe tensors for the matrix. Also obtained in real-form are the constant fourth-rank Eshelby’s tensor inside the elliptical inclusion, the hoop stress vectors and hoop stresses along the elliptical interface on both the matrix and inclusion sides, as well as the strain energy per unit height of the composite.

Keywords
inhomogeneous elliptical inclusion, eigenstrain, uniform field, Eshelby's tensor, hoop stress, strain energy, anisotropic elasticity, Stroh formalism
Milestones
Received: 11 November 2021
Revised: 13 January 2022
Accepted: 18 January 2022
Published: 10 December 2022
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton
Canada