Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid

Mélanie Otténio (1, 2) , Michel Destrade (1) , Raymond W. Ogden (2)

1 LMM - Laboratoire de modélisation en mécanique
2 Departments of Mathematics

We analyse the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space. One aim is to derive rigorously the incremental boundary conditions at the interface; this derivation is delicate because of the interplay between the Lagrangian and the Eulerian descriptions but is crucial for numerous problems concerned with the interaction between a compliant wall and a viscous fluid. A second aim of this work is to model the ultrasonic waves used in the assessment of aortic aneurysms, and here we find that for this purpose the half-space idealization is justified at high frequencies. A third goal is to shed some light on the stability behaviour in compression of the solid half-space, as compared with the situation in the absence of fluid; we find that the usual technique of seeking standing waves solutions is not appropriate when the half-space is in contact with a fluid; in fact, a correct analysis reveals that the presence of a viscous fluid makes a compressed neo-Hookean half-space slightly more stable. For a wave travelling in a direction of principal strain, we obtain results for the case of a general (incompressible isotropic) strain-energy function. For a wave travelling parallel to the interface and in an arbitrary direction in a plane of principal strain, we specialize the analysis to the neo-Hookean strain-energy function.

Mots clés: Acoustic waves; Interface waves; Elastic pre-stress; Fluid-solid interaction

Domaines: Dynamique des Fluides [physics.flu-dyn]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Mélanie Otténio, Michel Destrade, Raymond W. Ogden. Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid. International Journal of Non-Linear Mechanics, 2007, 42 (2), pp.310-320. ⟨10.1016/j.ijnonlinmec.2006.10.001⟩. ⟨hal-00192338⟩