Variations sur un thème de Biot - Une nouvelle formulation déplacement pour les matériaux poreux

Une nouvelle formulation du modèle de Biot pour les matériaux poroélastiques est ici proposée, cette formulation diffère par le choix des coordonnées généralisées. Elles sont choisies de manière à simplifier l'expression de l'énergie de déformation. Il est à noter qu'aucune hypothèse supplémentaire n'est ainsi formulée. Cette simplification du formalisme est étendue aux résultats classiques de la théorie de Biot. Une adaptation rigoureuse des modèles fluide équivalent et limp découle alors naturellement du nouveau formalisme. Il est aussi montré que dans le cas particulier de matériaux acoustiques, des simplifications additionnelles du formalisme peuvent être obtenues

Generalized equation for transient-wave propagation in continuous inhomogeneous rigid-frame porous materials at low frequencies

International audienceThis paper provides a temporal model for the propagation of transient acoustic waves in continuous inhomogeneous isotropic porous material having a rigid frame at low frequency range. A temporal equivalent fluid model in which the acoustic wave propagates only in the fluid saturating the material, is considered. In this model, the inertial effects are described by the inhomogeneous inertial factor [A.N. Norris., J. Wave Mat. Interact. 1 365 (1986)]. The viscous and thermal losses of the medium are described by two inhomogeneous susceptibility kernels which depend on the viscous and thermal permeabilities . The medium is one dimensional and its physical parameters (porosity, inertial factor, viscous and thermal permeabilities) are depth dependent. A generalized wave propagation equation in continuous inhomogeneous material is established and discussed

An alternative Biot’s displacement formulation for porous materials

International audienc

Porous and stratified porous media linear models of propagation: Propagation equations in the time domain

ISBN: 9781848210745International audienc

Ultrasound characterization of bone tissues by poroelastic theories

International audienc

Simultaneous determination of porosity, tortuosity, viscous and thermal characteristic lengths of rigid porous materials

International audienceWe present an improved method for the characterization of air-saturated porous materials by simultaneous measurement of porosity, tortuosity, viscous and thermal characteristic lengths via ultrasonic transmission only. The proposed method is based on a temporal model of the direct and inverse scattering problem for the transient ultrasonic waves in a homogeneous isotropic slab of rigid porous material. The advantage of the proposed method is that the four parameters are determined simultaneously using just transmitted experimental wave from a porous material saturated by one gas (air). In addition, no relationship is assumed between the two characteristic lengths

Acoustic characterization of air saturated porous materials at audible frequencies

International audienceAn acoustic method based on sound transmission is proposed for measuring the viscous and thermal permeability, viscous and thermal tortuosity, and porosity of porous materials having a rigid frame at low frequencies. The proposed method is based on a temporal model of the direct and inverse scattering problems for the propagation of transient audible frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The acoustic parameters are determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams

Modélisation de la propagation acoustique dans un mi- lieux poreux à structure rigide en basses fréquences.

National audienceDans ce travail, nous étudions la résolution des problèmes direct et inverse pour la propagation d'une onde acoustique dans un matériau poreux à structure rigide en régime basse fréquence. Les paramètres physiques décrivant la propagation dans ce modèle sont : les perméabilités visqueuse et thermique, le paramètre intertiel et la tortuosité thermique. Un nouveau paramètre décrivant les échanges visqueux entre fluide et structure est introduit dans le développement de la perméabilité dynamique basse fréquence. Des tests expérimentaux sur des ondes transmises sont effectués dans un guide. Des comparaisons avec des données théoriques sont aussi données

Measuring permeability of porous materials at low frequency range via acoustic transmitted waves

International audienc

Transient acoustic wave propagation in air-saturated porous media at low frequencies

International audienceThis paper provides a temporal model of the direct scattering problem for the propagation of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. In this model, the inertial effects are described by the low frequency approximation of the tortuosity. The viscous and thermal losses of the medium are modeled by viscous and thermal permeabilities. The propagation equation is derived and solved analytically in the time domain. An original expression of Green's function of the porous medium is obtained. The transmission scattering operator of the first transmitted wave is calculated and compared with experimental data