A novel foam structure is presented, which exhibits a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.

http://science.sciencemag.org/content/sci/235/4792/1038.full.pdf

Foam structures with a negative poisson's ratio

Poisson's ratio is, for specified directions, the ratio of a lateral contraction to the longitudinal extension during the stretching of a material Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, this property is generally believed to be rare in crystalline solids1 In contrast to this belief, 69% of the cubic elemental metals have a negative Poisson's ratio when stretched along the [110] direction For these metals, we find that correlations exist between the work function and the extremal values of Poisson's ratio for this stretch direction, which we explain using a simple electron-gas model Moreover, these negative Poisson's ratios permit the existence, in the orthogonal lateral direction, of positive Poisson's ratios up to the stability limit of 2 for cubic crystals Such metals having negative Poisson's ratios may find application as electrodes that amplify the response of piezoelectric sensors

Negative Poisson's ratios as a common feature of cubic metals

Poisson’s ratio is defined as the lateral contraction strain in a solid divided by the longitudinal extension strain measured in a simple tension experiment. In almost all materials Poisson’s ratio, usually denoted by v, is positive. For isotropic materials (those in which the properties are independent of direction), energy arguments in the theory of elasticity[’] may be used to show that 1 2 v I 112. The relationship between shear modulus G, bulk modulus K, and Poisson’s ratio v for isotropic materials is given by Equation (1).

Advances in negative Poisson's ratio materials

Foam materials based on metal and several polymers were transformed so that their cellular architecture became re-entrant, i.e. with inwardly protruding cell ribs. Foams with re-entrant structures exhibited negative Poisson's ratios as well as greater resilience than conventional foams. Foams with negative Poisson's ratios were prepared using different techniques and materials and their mechanical behaviour and structure evaluated.

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Negative Poisson's ratio polymeric and metallic foams

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

https://iopscience.iop.org/article/10.1088/0034-4885/76/12/126501/pdf

Metamaterials beyond electromagnetism

A method of calculating the anisotropy of Poisson's ratio is applied to trigonal and tetragonal crystals in the literature. The method of calculation is extended to hexagonal crystals. The results are illustrated by reference to Tl and Cd.

Y. Li

Papers

The anisotropic behavior of Poisson's ratio, Young's modulus, and shear modulus in hexagonal materials