Non-locality of the Willis coupling in fluid laminates

The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to Padé approximation transfer matrix. A second-order Taylor expansion matrix elements exhibits Willis coupling. This coupling is sum a local term and nonlocal term. arises from apparent bulk modulus quasi one-dimensional problems. nonlocality directly impacts governing equations modeling acoustic wave propagation these materials, which then involve convolution products space. As an example, two-orthotropic porous material laminate considered. theoretically scattering coefficients found excellent agreement with those numerically calculated. widens frequency range validity accuracy thus calculated when compared classical homogenization results for absent. widening mostly relies on effect impedance laminate. finally general