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An elliptical incompressible liquid inclusion in an infinite anisotropic elastic space

Xu Wang and Peter Schiavone
Vol. 12 (2024), No. 2, 217–232
DOI: 10.2140/memocs.2024.12.217
Abstract

Using the Stroh sextic formalism, we analyze the generalized plane strain problem associated with an elliptical incompressible liquid inclusion in an infinite anisotropic elastic matrix subjected to a uniform loading at infinity. A real-form solution of the internal uniform hydrostatic stresses, strains and rigid body rotation within the liquid inclusion is obtained in terms of the Barnett–Lothe tensors and the fundamental elasticity matrix for the surrounding matrix. Real-form expressions for the hoop stress vector and hoop stress along the elliptical interface on the matrix side are also obtained. Explicit results are derived for an orthotropic elastic matrix with isotropy as a special case.

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Keywords
elliptical incompressible liquid inclusion, uniform field, anisotropic elasticity, generalized plane strain deformation, Stroh formalism, real-form solution
Mathematical Subject Classification
Primary: 74B99, 74E05, 74E10
Secondary: 74A60, 74M25
Milestones
Received: 1 January 2024
Revised: 27 February 2024
Accepted: 15 April 2024
Published: 7 May 2024

Communicated by Francesco dell'Isola
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
Donadeo Innovation Center for Engineering
Edmonton
Canada
© 2024 MSP (Mathematical Sciences Publishers).