Elastic instability of soft cellular solids plays an increasingly important role in the creation of metamaterials with smart properties. Inspiration for much of this research comes from a planar metamaterial with negative Poisson's ratio behavior induced by elastic instability. Here we extend the concept of buckling induced pattern switch further to the design of a new series of three-dimensional metamaterials with negative Poisson's ratio over a large strain range. The highlight of this work is that our designs are based on very simple initial geometric shapes.Different deformation patterns of materials without and with auxetic behavior.

Auxetic metamaterials are synthetic materials with microstructures engineered to achieve negative Poisson's ratios. There has been intense interest in auxetic metamaterials due to their unusual properties and many potential applications. However, most of the previous research was focused on auxetic behaviour of elastomers under elastic deformations. Inspired by our recent finding of the loss of auxetic behaviour in auxetic metamaterials when the base material was changed from elastomer to metal, we have carried out a series of experiments and finite element simulations to investigate the mechanism behind this phenomenon. Employing an improved methodology of generating buckling-induced auxetic metamaterials, several samples of metallic auxetic metamaterials have been fabricated using 3D printing technique. Furthermore, parametric studies have been performed through experimentally validated finite element models to explore the auxetic performance of the designed metamaterials. It is found that the auxetic performance can be tuned by the geometry of microstructures; and the strength and stiffness can be tuned by the plasticity of the base material while maintaining the auxetic performance.

Recent advances in additive manufacturing make it possible to fabricate periodic lattice structures with complex configurations. However, a proper design strategy to achieve lattice structures with controlled anisotropy is still unavailable. There is an urgent need to fill this knowledge gap in order to develop mechanical metamaterials with prescribed properties. Here we propose two different methodologies to design lattice structures with controlled anisotropy. As examples, we created two new families of lattice structures with isotropic elasticity and cubic symmetric geometry. The findings of this work provide simple and effective strategies for exploring lightweight metamaterials with desired mechanical properties.

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A recent analysis by Pendry [J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] shows that a dielectric slab with a dielectric constant ε=−1 can produce a perfect image in the electrostatic limit (c→∞), independent of the permeability μ, and therefore is a perfect lens. Here we include retardation effects and show how distance and dissipation make the lens no longer perfect. Nevertheless we conclude that very significant improvements over conventional near field imaging may be obtained in the microwave regime.