An anisotropic elastic inhomogeneous elliptical inclusion

Wang, Xu; Schiavone, Peter

doi:10.2140/jomms.2022.17.181

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An anisotropic elastic inhomogeneous elliptical inclusion

Xu Wang and Peter Schiavone

Vol. 17 (2022), No. 2, 181–192

DOI: 10.2140/jomms.2022.17.181

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

Vol. 17, No. 2, 2022

Xu Wang and Peter Schiavone

Abstract

Keywords

Milestones

Authors