A rational procedure for the experimental evaluation of the elastic coefficients in a linearized formulation of biphasic media with compressible constituents

This article illustrates the specialization to infinitesimal perturbations of the geometrically nonlinear formulation describing the macroscopic dynamic behavior of biphasic media presented in (Serpieri and Rosati J Mech Phys Solids 59(4):841–862, 2011) where, based on Lagrangian mechanics arguments, a consistent mathematical theory of fluidsaturated poroelastic material is developed accounting for the property that both constituent materials are microscopically compressible. The primary contribution of this work is the employment of the linearized model in the development of a general procedure for the determination of the relevant elastic coefficients on the basis of the data provided by a set of experimental measures analogous to the one originally considered by Biot and Willis consisting of a shear test, an unjacketed compressibility test and two jacketed tests in which drainage is either completely allowed or prevented. The linearization of the formulation is first presented for a generic configuration in which both phases are undergoing a generic motion. Subsequently, a specific study is presented on the case that the media is motionless, homogeneous, and isotropic in the reference configuration, which is typical of common experimental set-ups for static tests. A numerical example is shown and a general relation between the elastic coefficients and Biot’s constant is derived which consistently accounts for the compressibility of all materials.