Role of material mismatch on the linear poroelastic response investigated through an assemblage of a two-dimensional circular inclusion embedded in an infinite medium subjected to far-field loading

The present work concerns the semi-analytical computation of stress-field and pore pressure in a two-dimensional linear poroelastic material comprising of a circular inclusion embedded in an infinite plane and subjected to far-field loading under mechanical equilibrium. A combination of Laplace transform, loading based angular dependence for the field quantities and Principle of Superposition allows for closed form solution of quantities of interest in Laplace domain. Stress and pore pressure in time domain is recovered using limit theorems for short and long time and through numerical inversion for intermediate time. Utility of the developed solution is demonstrated through the role of variation in material properties of inclusion and matrix on the stress concentration along the matrix-inclusion interface.