On the limits of an “in vacuum” model to determine the mechanical parameters of isotropic poroelastic materials

The prediction of the acoustic performance of multi-layered structures involving porous materials now classically relies on the use of Biotʹs theory for the modelling of the porous medium. In particular, it is of prime importance to correctly assess the mechanical parameters of the porous skeleton “in vacuum”. However, measurements of these parameters “in vacuum” conditions comprises some problems so that they are commonly carried out in ambient conditions assuming that the response of the porous material is not influenced by its fluid phase and solely determined by the parameters of its solid phase. The purpose of this work is to investigate the conditions when a mechanically excited porous material exhibits indeed an “in vacuum” behaviour. The comparison between the air-saturated and the “in vacuum” models is carried out both in the case of impedance infinite models and taking into account finite lateral dimensions of the porous sample. It is shown that a model accounting for finite dimensions of the porous samples must be considered in order that Biotʹs and “in vacuum” models yield identical mechanical responses. More precisely, a “poroelastic” shape factor defined as the ratio of the volume of the porous sample to the area of its free lateral sides is introduced to quantify the mismatch between the two models. For small values of this parameter, the mechanical response of the porous material calculated using Biotʹs model is similar to the one predicted using the “in vacuum” model. For higher values, the responses calculated by the two models exhibit noticeable differences. The corresponding limiting value of the poroelastic shape factor is shown to depend on the flow resistivity together with the thickness of the porous sample.