Classical and higher order interface conditions in poroelasticity

The paper deals with the derivation of non classical interface conditions in linear poroelasticity in the framework of the quasi-static diphasic Biot’s model. More precisely, we analyze the mechanical behavior of two linear isotropic poroelastic solids, bonded together by a thin layer, constituted by a linear isotropic poroelastic material, by means of an asymptotic analysis. After defining a small parameter ε, which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems, the so-called soft, hard and rigid poroelastic interface models, respectively. First and higher order interface models are derived. Moreover, we identify the non classical transmission conditions at the interface between the two three-dimensional bodies in terms of the jump of the stresses, specific discharge, pressure and displacements.