A coated elliptical compressible liquid inclusion

Abstract

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.