On three-dimensional dilational elastic metamaterials

Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial material, a metamaterial, which approaches the ideal of a dilational material. The main novelty of our work is that we also fabricate and characterize corresponding metamaterial samples. To reveal all modes in the design, we calculate the phonon band structures. On this basis, using cubic symmetry we can unambiguously retrieve all different non-zero elements of the rank-four effective metamaterial elasticity tensor from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches -1 in the limit of small internal connections. This finding is also supported by independent, static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as -0.8 in good agreement with the theory. Microscopic samples are also presented.