Non-locality of the Willis coupling in fluid laminates

International audience ; The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to the Padé approximation of the transfer matrix. A secondorder Taylor expansion of the transfer matrix elements exhibits Willis coupling. This coupling is the sum of a local term and a nonlocal term. The nonlocal term arises from the apparent bulk modulus in quasi one-dimensional problems. The nonlocality directly impacts the governing equations modeling the acoustic wave propagation in these Willis materials, which then involve convolution products in space. As an example, a two-orthotropic porous material laminate