Convergence of poroelastic finite elements based on Biot displacement formulation

Nicolas Dauchez (1) , Sohbi Sahraoui (1) , Noureddine Atalla (2)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans
2 GAUS - Groupe d'Acoustique de l'Université de Sherbrooke

The convergence of linear poroelastic elements based on Biot displacement formulation is investigated. The aim is to determine a mesh criterion that provides reliable results under a given frequency limit. The first part deals with 1D applications for which resonance frequencies can be related to Biot wavelengths. Their relative contributions to the motion are given in order to determine if the mesh criteria for monophasic media are suitable for poroelastic media. The imposition of six linear elements per wavelength is found for each Biot wave as a primary condition for convergence. For 3D applications, convergence rules are derived from a generic configuration, i.e., a clamped porous layer. Because of the complex deformation, the previous criterion is shown to be insufficient. Influence of the coupling between the two phases is demonstrated.

Mots clés: vibroacoustics; porous material; Biot model; finite element method; convergence

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Nicolas Dauchez, Sohbi Sahraoui, Noureddine Atalla. Convergence of poroelastic finite elements based on Biot displacement formulation. Journal of the Acoustical Society of America, 2001, 109 (1), pp.33-40. ⟨10.1121/1.1289924⟩. ⟨hal-00438864⟩