Homogenization models for thin rigid structured surfaces and films

Jean-Jacques Marigo (1) , Agnès Maurel (2)

1 LMS - Laboratoire de mécanique des solides
2 IL - Institut Langevin - Ondes et Images (UMR7587)

A homogenization method for thin microstructured surfaces and films is presented. In both cases, sound hard materials are considered, associated with Neumann boundary conditions and the wave equation in the time domain is examined. For a structured surface, a boundary condition is obtained on an equivalent flat wall, which links the acoustic velocity to its normal and tangential derivatives (of the Myers type). For a structured film, jump conditions are obtained for the acoustic pressure and the normal velocity across an equivalent interface (of the Ventcels type). This interface homog-enization is based on a matched asymptotic expansion technique, and differs slightly from the classical homogenization, which is known to fail for small structuration thicknesses. In order to get insight into what causes this failure, a two-step homogenization is proposed, mixing classical ho-mogenization and matched asymptotic expansion. Results of the two homogenizations are analyzed in light of the associated elementary problems, which correspond to problems of fluid mechanics, namely, potential flows around rigid obstacles.

Domaines: Mécanique des solides [physics.class-ph]

Jean-Jacques Marigo, Agnès Maurel. Homogenization models for thin rigid structured surfaces and films. Journal of the Acoustical Society of America, 2016, 140 (1), pp.260-273. ⟨10.1121/1.4954756⟩. ⟨hal-01657581⟩