Materials and structures with negative Poisson's ratio exhibit a counter-intuitive behaviour. Under uniaxial compression (tension), these materials and structures contract (expand) transversely. The materials and structures that possess this feature are also termed as 'auxetics'. Many desirable properties resulting from this uncommon behaviour are reported. These superior properties offer auxetics broad potential applications in the fields of smart filters, sensors, medical devices and protective equipment. However, there are still challenging problems which impede a wider application of auxetic materials. This review paper mainly focuses on the relationships among structures, materials, properties and applications of auxetic metamaterials and structures. The previous works of auxetics are extensively reviewed, including different auxetic cellular models, naturally observed auxetic behaviour, different desirable properties of auxetics, and potential applications. In particular, metallic auxetic materials and a methodology for generating 3D metallic auxetic materials are reviewed in details. Although most of the literature mentions that auxetic materials possess superior properties, very few types of auxetic materials have been fabricated and implemented for practical applications. Here, the challenges and future work on the topic of auxetics are also presented to inspire prospective research work. This review article covers the most recent progress of auxetic metamaterials and auxetic structures. More importantly, several drawbacks of auxetics are also presented to caution researchers in the future study.

Auxetic metamaterials and structures: a review

Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review

The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. Although this value can theoretically be negative, it is positive for nearly all materials, though negative values have been observed in so-called auxetic structures. However, nearly all auxetic materials are bulk materials whose microstructure has been specifically engineered to generate a negative Poisson's ratio. Here we report using first-principles calculations the existence of a negative Poisson's ratio in a single-layer, two-dimensional material, black phosphorus. In contrast to engineered bulk auxetics, this behaviour is intrinsic for single-layer black phosphorus, and originates from its puckered structure, where the pucker can be regarded as a re-entrant structure that is comprised of two coupled orthogonal hinges. As a result of this atomic structure, a negative Poisson's ratio is observed in the out-of-plane direction under uniaxial deformation in the direction parallel to the pucker.

/pdf/negative-poisson-s-ratio-in-single-layer-black-phosphorus-3i0kyfwpwv.pdf

Negative poisson’s ratio in single-layer black phosphorus

In the past decade, mechanical metamaterials have garnered increasing attention owing to its novel design principles which combine the concept of hierarchical architecture with material size effects at micro/nanoscale. This strategy is demonstrated to exhibit superior mechanical performance that allows us to colonize unexplored regions in the material property space, including ultrahigh strength‐to‐density ratios, extraordinary resilience, and energy absorption capabilities with brittle constituents. In the recent years, metamaterials with unprecedented mechanical behaviors such as negative Poisson's ratio, twisting under uniaxial forces, and negative thermal expansion are also realized. This paves a new pathway for a wide variety of multifunctional applications, for example, in energy storage, biomedical, acoustics, photonics, and thermal management. Herein, the fundamental scientific theories behind this class of novel metamaterials, along with their fabrication techniques and potential engineering applications beyond mechanics are reviewed. Explored examples include the recent progresses for both mechanical and functional applications. Finally, the current challenges and future developments in this emerging field is discussed as well.

Mechanical Metamaterials and Their Engineering Applications

The surge of interest in so-called “designer materials” during the last few years together with recent advances in additive manufacturing (3D printing) techniques that enable fabrication of materials with arbitrarily complex nano/micro-architecture have attracted increasing attention to the concept of mechanical metamaterials. Owing to their rationally designed nano/micro-architecture, mechanical metamaterials exhibit unusual properties at the macro-scale. These unusual mechanical properties could be exploited for the development of materials with advanced functionalities, with applications in soft robotics, biomedicine, soft electronics, acoustic cloaking, etc. Auxetic mechanical metamaterials are identified by a negative Poisson's ratio and are perhaps the most widely studied type of mechanical metamaterials. Similar to other types of mechanical metamaterials, the negative Poisson's ratio of auxetics is generally a direct consequence of the topology of their nano/micro-architecture. This paper therefore focuses on the topology–property relationship in three main classes of auxetic metamaterials, namely re-entrant, chiral, and rotating (semi-) rigid structures. While the deformation mechanisms in the above-mentioned types of structures and their relationship with the large-scale mechanical properties receive most attention, the emerging concepts in design of auxetics such as the use of instability in soft matter and origami-based structures are discussed as well. Furthermore, the data available in the literature regarding the elastic properties of auxetic mechanical metamaterials are systematically analyzed to identify the spread of Young's modulus–Poisson's ratio duos achieved in the auxetic materials developed to date.

/pdf/auxetic-mechanical-metamaterials-1gbq3f4vkw.pdf

Auxetic mechanical metamaterials

http://silver.neep.wisc.edu/~lakes/PoissonChiral.pdf

Properties of a chiral honeycomb with a poisson's ratio of — 1

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Properties of a chiral honeycomb with a poisson's ratio of — 1