On Saint-Venantʹs principle for a linear poroelastic material in plane strain

In this paper we consider the state of plane strain in an elastic material with voids occupying a rectangular strip. Such a strip is maintained in equilibrium under self-equilibrated traction and equilibrated force applied on one of the edges, while the other three edges are traction-free and subjected to zero volumetric fraction or zero equilibrated force. Our aim is to derive some explicit spatial estimates describing how some appropriate measures of a specific Airy stress function and volume fraction evolve with respect to the distance to the loaded edge. The both cases of homogeneous and inhomogeneous poroelastic materials are considered. The results of the present paper prove how the spatial-decay rate varies with the constitutive profile.