Two non‐circular compressible liquid inclusions in an infinite elastic matrix

Abstract We derive an analytical solution to the plane strain problem associated with two interacting identical non‐circular compressible liquid inclusions embedded 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 using a conformal mapping function for quadrature domains by Crowdy (2015) and the technique of analytic continuation. The internal uniform hydrostatic stress field within each one of the two equal symmetric liquid inclusions and the hoop stress along each liquid‐solid interface on the matrix side are studied in detail.