A coated elliptical compressible liquid inclusion

We study the plane strain problem of a three-phase composite consisting of an internal elliptical compressible liquid inclusion, an intermediate isotropic elastic coating and an outer unbounded isotropic elastic matrix subjected to uniform remote in-plane normal stresses. The perfect liquid–solid an...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) Vol. 95; no. 4; p. 83
Main Authors: Wang, Xu, Schiavone, Peter
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025
Springer Nature B.V
Subjects:
Aspect ratio
Boundary value problems
Classical Mechanics
Coating
Compressibility
Conformal mapping
Elastic properties
Ellipses
Engineering
Exact solutions
Hoop stress
Hoops
Interfaces
Liquid-solid interfaces
Mathematical problems
Normal stress
Original
Plane strain
Stress concentration
Stress distribution
Theoretical and Applied Mechanics
Constant hoop stress
Internal uniform hydrostatic stress
Elliptical compressible liquid inclusion
Elastic coating
Analytical solution
Complex variable method
ISSN:0939-1533, 1432-0681
Online Access:Get full text
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Summary:We study the plane strain problem of a three-phase composite consisting of an internal elliptical compressible liquid inclusion, an intermediate isotropic elastic coating and an outer unbounded isotropic elastic matrix subjected to uniform remote in-plane normal stresses. The perfect liquid–solid and solid–solid interfaces comprise two confocal ellipses. An analytical solution in series form is derived using conformal mapping and analytic continuation. Furthermore, when the compressibility of the liquid inclusion is chosen according to prescribed elastic constants of the coating and the matrix and the given thickness of the coating, we achieve a constant distribution of hoop stress along the entire elliptical liquid–solid interface on the coating side under a remote hydrostatic load. In this case, the compressibility of the liquid inclusion, the internal uniform hydrostatic stress field within the liquid inclusion and the constant hoop stress along the entire liquid–solid interface on the coating side are all unaffected by the aspect ratio of the elliptical inclusion.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-025-02791-x