Validity of the one-dimensional limp model for porous materials

TL;DR

This paper proposes a simple criterion based on a new parameter, FSI, to determine when the one-dimensional limp model accurately describes porous materials, improving modeling efficiency.

Contribution

It introduces the Frame Stiffness Influence (FSI) parameter and a criterion to assess limp model validity for porous materials.

Findings

The FSI parameter effectively predicts limp model applicability.

Critical FSI values are established for specific boundary conditions.

The criterion simplifies the decision process for using the limp model.

Abstract

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.