Abstract
Homogenization schemes for wave propagation in heterogeneous electromagnetic (EM) and elastic materials indicate that EM bianisotropy and elastic momentum-strain and stress-velocity field coupling is required to correctly describe the effective behavior of the medium [Alu, Phys. Rev. B, 84, 075153 (2011); Milton and Willis, Proc. R. Soc. A, 463, 855–880, (2007)]. Further, the determination of material coupling terms in EM resolves apparent violations of causality and passivity which is present in earlier models [A. Alù, Phys. Rev. B, 83, 081102(R) (2011)]. These details have not received much attention in fluid acoustics, but they are important for a proper description of acoustic metamaterial behavior. We derive expressions for effective properties of a heterogeneous fluid medium from expressions for the conservation of mass, the conservation of momentum, and the equation of state and find a physically meaningful effective material response from first-principles. The results show inherent coupling between the ensemble averaged volume strain-momentum and pressure-velocity field. The approach is valid for an infinite periodic lattice of heterogeneities and employs zero-, first-, and second-order tensorial Green’s functions to relate point-discontinuities in compressibility and density to far field pressure and particle velocity fields. [This work was supported by the Office of Naval Research.]
Published Version
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