Supplementary material from "An elliptical liquid inclusion in an infinite elastic plane"
Jianzhang Wu, C. Q. Ru, L. Zhang · Figshare · 2018
Beyond recent related literatures which focused on spherical incompressible liquid inclusions, the present work studies an elliptical compressible liquid inclusion in an infinite elastic plane under static remote mechanical loading. Here, it is assumed that the change of pressure inside the liquid inclusion is linearly related to the change of inclusion volume with the bulk modulus of the liquid as the proportionality coefficient. Also, the role of liquid surface tension on the solid–liquid interface is examined especially when the size of liquid inclusion is comparable to or smaller than the elastocapillary length. Our results showed that both the surface tension and the change of liquid pressure have a significant effect to reduce stress concentration factor at the endpoints of an elliptical liquid inclusion. In addition, the pressure change inside the liquid inclusion is studied when a uniaxial remote stress applied perpendicular or parallel to the major axis of the elliptical liquid inclusion. In particular, the effective plane-strain Young's modulus of a solid–liquid composite containing circular liquid inclusions predicted by the present model is linearly related to the volume fraction of the liquid inclusions, in reasonable agreement with existing experimental data.