An Elliptical Incompressible Liquid Inclusion in a Compressible Hyperelastic Solid of Harmonic Type

A complete closed-form solution is derived to the finite plane elasticity problem associated with an elliptical incompressible liquid inclusion embedded in an infinite compressible hyperelastic matrix of harmonic type subjected to uniform remote in-plane Piola stresses. The internal uniform hydrostatic Piola stresses and deformation gradients within the elliptical incompressible liquid inclusion are obtained. The internal uniform hydrostatic tension and hoop stress on the matrix side along the liquid-solid interface for various shapes of the elliptical liquid inclusion and different elastic constants of the matrix under various remote loadings are calculated.