title: Closed-cell crystalline foams: self-assembling, resonant metamaterials.
abstract: 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. Recently self-assembly techniques have been implemented to produce such foams: a Kelvin (body centered cubic) foam, a face centered cubic foam, and a Weaire-Phelan structure. Numerical models are employed to demonstrate that such foams are superanisotropic, selectively behaving as a fluid or a solid, pentamode solids as a result of fluid-structure interaction, in addition to having regimes characterized by film resonances and high density of states. Microstructural deformations obtained from numerical models allow the derivation of equivalent mechanical models.
authors.affiliation: Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Spadoni
authors.affiliation: Université Paris 6, UMR 7588 CNRS-UPMC, INSP 4, Place Jussieu, 75252 Paris cedex 05, France.
authors.forename: Reinhard
authors.initials: R
authors.lastname: Höhler
authors.affiliation: Université Paris 6, UMR 7588 CNRS-UPMC, INSP 4, Place Jussieu, 75252 Paris cedex 05, France.
authors.forename: Sylvie
authors.initials: S
authors.lastname: Cohen-Addad
authors.affiliation: Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Dorodnitsyn