A symmetric liquid lip inclusion in an infinite isotropic elastic matrix

We study the plane strain problem of a symmetric compressible liquid lip inclusion with two cusps in an infinite isotropic elastic matrix subjected to uniform remote in-plane normal stresses. The pair of analytic functions characterizing the elastic field in the matrix is derived in closed form. Explicit, elementary, and concise expressions in terms of the two Skempton's induced pore-pressure coefficients are obtained for the internal uniform hydrostatic tension within the liquid inclusion and the mode I stress intensity factor at the cusp tip. When the two remote normal stresses satisfy a single condition, the external loading will not induce any singular stress field at the cusp tips.