Analytical analysis of slow and fast pressure waves in a two-dimensional cellular solid with fluid-filled cells.

Wave propagation in cellular and porous media is widely studied due to its abundance in nature and industrial applications. Biot's theory for open-cell media predicts the existence of two simultaneous pressure waves, distinguished by its velocity. A fast wave travels through the solid matrix, whereas a much slower wave is carried by fluid channels.

Closed-cell crystalline foams: self-assembling, resonant metamaterials.

Internal degrees of freedom and periodic structure are critical requirements in the design of acoustic/elastic metamaterials since they can give rise to extraordinary properties like negative effective mass and stiffness. However, they are challenging to realize in three dimensions. Closed-cell, crystalline foams are a particularly advantageous basis to develop metamaterials as they intrinsically have a complex microstructure, exhibiting internal resonances.