it is compressed, because it has a negative Poisson's ratio. This report briefly reviews These auxetic materials also offer very good sound and vibration absorption and However, more research work needs to be done for further .. effect in many mechanical properties such as in-plane indentation resistance, transverse. Aug 9, This is particularly true for auxetic material designs, such as the prototypical re- entrant upon the local deflected shape of the beam, yielding a complex relationship. .. Auxetic materials: the positive side of being negative. In common, all materials possess positive Poisson's ratio, i.e. the materials shrink .. Relationship between angle u and angle a. Fig. Poisson's ratio of . [10] Evans KE, Anderson KL. Auxetic materials: the positive side of being negative.

The distinction is shown in a map adapted from G. The name auxetic, or auxetics, after Evans and co-workers in the U. The paper that introduced this term provided a proposal for achieving such effects at the molecular scale via a two dimensional model resembling the bow tie structure of negative Poisson's ratio honeycomb.

As for early experiments by this group, highly anisotropic expanded porous polytetrafluoroethylene was found to exhibit a negative Poisson's ratio [5]. More recently the terms metamaterial and architected material have been used for materials with complex designed structure.

Description Novel materials are presented, which exhibit a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.

The original negative Poisson's ratio foam was developed by Rod Lakes.

### Stiff auxetics: Hierarchy as a route to stiff, strong lattice based auxetic meta-materials

The cause of the negative Poisson's ratio is non-affine deformation. In a conceptual advance [3], laminate structures were presented by Milton. These laminates give rise to intentional negative Poisson's ratios combined with mechanical isotropy in two dimensions or in three dimensions [3]. These laminates have structure on several levels of scale; they are hierarchical. By appropriate choice of constituent properties one can achieve Poisson's ratios approaching the lower limit of The laminate Poisson's ratio is close to the rigorous lower bound which is independent of the microstructure, therefore it will not be possible to find microstructures with much lower Poisson's ratio for given constituent stiffnesses Review articles on auxetic or dilational materials are given by Lakes in [6] and by Evans and Alderson in [7].

**Negative Poisson’s ratio: a rare find in battery materials**

A more recent review article is as follows. In comparing a material's resistance to distort under mechanical load rather than alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically.

With new experiments, computational methods and routes to materials synthesis, we assess what Poisson's ratio means in the contemporary understanding of the mechanical characteristics of modern materials. Central to these recent advances, we emphasize the significance of relationships outside the elastic limit between Poisson's ratio and densification, connectivity, ductility and the toughness of solids; and their association with the dynamic properties of the liquids from which they were condensed and into which they melt.

Lakes, "Foam structures with a negative Poisson's ratio", Science, [2] J. Milton"Composite materials with Poisson's ratios close to -1", J. Solids, 40,[4] K. Rogers, "Molecular network design", Nature, Evans, "Microporous materials with negative Poisson's ratio: Microstructure and mechanical properties", J. More references, negative Poisson's ratio or auxetics,top recent. There are other such special issues. Alderson Quantitative analysis of the microscale of auxetic foams p N.

Evans Auxetic behaviour from rotating rigid units p J. Hoover Thermal expansion and contraction of polymer thin films p T. Nishida Molecular dynamics study of the high-temperature elasticity of SiO2 polymorphs: Idzikowski Poisson's ratio of degenerate crystalline phases of three-dimensional hard dimers and hard cyclic trimers p M. Wojciechowski Simulation of a superconducting granular system on a honeycomb structure p G. Natali Al-based systems with unusual mechanical and transport properties p K.

Wojciechowski Expanding the range of auxetic polymeric products using a novel melt-spinning route p N.

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Davies Directional and band-gap behavior of periodic auxetic lattices p M. Scarpa Auxetic compliant flexible PU foams: Ruzzene Global and local linear buckling behavior of a chiral cellular structure p A. Stavroulakis Stereographic projections of Poisson's ratio in auxetic crystals p S. Tokmakova Monte Carlo simulation of two-dimensional hard body systems with extreme values of the Poisson's ratio p K.

Wojciechowski Design of auxetic polymer self-assemblies p Gaoyuan Wei Liquids at negative pressure p C.

### Names of negative Poisson's ratio materials: auxetic materials, anti-rubber, dilational materials

Molecular Simulation, v 31, n 13, Nov 1,p Dynamic simulations of potentially auxetic liquid-crystalline polymers incorporating swivelling mesogens Aldred, P. Molecular Simulation, v 31, n 13, Nov 1,p Modelling of the mechanical and mass transport properties of auxetic molecular sieves: An idealised inorganic zeolitic host-guest system Alderson, A.

Further, the ability to vary the hinge arc allows one to vary its Poisson's ratio properties for the same unit cell, yielding a critical bistable angle that transitions from positive to negative Poisson's ratio. Finally, the greater flexibility of the design enables a multistable latch-release structure to be developed in which orthogonal actuation and release of the latch storage mechanism have advantages compared to current bistable storage mechanisms with high-stress concentration Shan et al.

Materials and Methods 3D Printing Samples were manufactured using fused deposition modeling, a facile extrusion-based 3D printing technique. In this widely available technique, thermoplastic polymers are extruded in a layer-by-layer manner on a heated plate.

The standard MakerBot Replicator was used as the desktop 3D printer and 1. These viscoelastic filament polymers exhibit shear-thinning behavior that enables facile extrusion from the nozzle and subsequent cooling into the desired structure on the print bed. Figure S1A demonstrates the 3D printing set up used in this study. The samples were designed using SketchUp, a freely available 3D modeler, and written into a stereolithography file format STLwhich specifies tool path, print speed, retraction amount, and other factors that influence print quality.

To create the 3D structure, models were made by printing unit strips of multiple cells and then solvent welding them together to form an interdigitated 3D material. Mechanical Characterization For load-displacement measurements, a Tinius Olsen benchtop Hounsfield 5 kN tension-compression machine with a N load cell was used. To enable lateral movement of the samples due to auxetic property, the samples were lubricated with oil. It was found that this lubrication reduced the friction at the sample edges, and by comparing the experimental force-displacement results with the analytical equations, the reduced coefficient of static friction was found to be 0.

In our tests, the samples were not attached to the compression plates. As a result, in some of the measurements, there is a brief nonlinearity before the elastic response in the force-displacement curve.

This nonlinearity is not present in each measurement and indicates the brief change in contact between the sample and the compression plate. Each test was repeated multiple times and the results were in good agreement, demonstrating good repeatability.

To characterize the Poisson's ratio, the inwards movement of markers placed at the ends of the auxetic samples were measured as the samples were compressed a predetermined amount. The response of the material was captured using a linear elastic model with PLA filament values reported in literature; a Young's modulus of MPa and Poisson's ratio of 0. These values were used both in this finite element simulation and in the analytical calculations.

We applied a boundary condition of a downward 20 mm movement to one edge of the auxetic. This set simulated the movement of the compression plates in our force-displacement testing. The bottom edge of the structure was constrained with an ENCASTRE constraint to prevent vertical or horizontal movement, simulating the stationary bottom edge during the force-displacement testing.

In each simulation, the spatial displacement and reaction force in the relative x or y direction was monitored at the centralized reference point. This resulted in the simulation force-displacement curves shown above. Poisson's ratios were extracted in a similar manner by monitoring the displacement of the edges of the structure. The finite element simulation accurately models the elastic region of the auxetic deformations.

Figures 2A,B demonstrates the comparison between the experimental and simulation results. As depicted for both the honeycomb and the s-hinged auxetic deformed in the straight-edge direction, the simulation is in agreement with the experimental data until the yield point of PLA. Results and Discussion S-Shape Hinge The novel stress-delocalization design was inspired by a smooth hinge geometry in nature, which minimizes stress concentration by distributing it through the length of the hinge.

We applied the concept to replace the straight edges of the conventional reentrant honeycomb with optimally deforming redesigned arcs between the solid ribs Figure 1A. These arcs were calculated with an appropriate radius and arc length that enable the greatest range of deformation, while staying within the elastic limit of PLA printer filament, and exhibit a much larger range of deformation compared to the conventional honeycomb Figures 1B,C.

Fabrication of s-hinged unit cell into a 2D and 3D auxetic material. A S-hinged unit cell dashed overlaid on comparison of a reentrant honeycomb unit cell solid blue. B Compressed reentrant honeycomb auxetic with outline of original cell, stresses concentrate at vertices. C Compressed s-hinged auxetic made from degree arc length with outline of original cell, stresses distribute with deformation of the whole hinge.

To illustrate the benefits of this new auxetic design, we also fabricated a conventional auxetic honeycomb structure with the same unit cell size and reentrant angle for valid comparison. We note that this 3D printing procedure is particularly well suited to demonstrate advantages of our s-hinge geometric design because common defects, such as rounded corners or poorly connected nodes that occur when using one continuous filament to print sharp edges, are prevented by printing the curved structure.

Stress Distribution in S-Hinge Structure We combined experimental testing and finite element FE simulations to determine both the macroscopic and local stress and strain behavior in the s-hinge compared to the conventional honeycomb. The experimental and FE models are in good agreement Figures 2A,Bshowing that the model faithfully captures the physics of the deformation. In contrast, the s-hinge structure delocalizes the stress concentration, reaching a maximum local von Mises stress of 8 MPa at that same macroscopic compression Figure 2D.

The s-hinge structure also enables a lower equivalent plastic strain Figure S3. Experimental and FE simulation characterization of conventional honeycomb and s-hinge auxetics. The good agreement of results from the experimental and FE simulations for the A conventional honeycomb and B s-hinge structures validate the finite element models developed for the structures. The orange outline represents the original undeformed cell.

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F Macroscopic strain vs. This stress and strain minimization through the s-hinge design allows a wider range of materials to be used for the auxetic structure. This property of the s-hinged structure would enable more materials, such as glass fibers, ceramics, and other brittle materials with small elastic regions that were previously difficult to apply in auxetic geometries, to be used as auxetics, while still achieving a large macroscopic reversible strain.

Plastic deformation, even in the absence of a large deviation from elastic behavior, leads to damage and its effects can be seen upon repeated compressive cycling. Deformation Characterization of S-Hinge Structure The stress versus strain curve in Figure 2F summarizes the mechanical behavior of the two geometries in compression, for which our structure is optimized. The initial linear region in both curves demonstrates the structure's elastic regime. The conventional honeycomb is much stiffer and quickly reaches its elastic limit, where the sharp peak denotes plastic collapse of the beams and the subsequent spikes show softening and hardening of the structure that occur during the breaking and collapse of different sets of beams.

We note that for extending these principles to extension, one should smoothen the connection where the s-hinges meet with the straight-edge linking segments. Though not in the scope of this work, introducing another smooth joint would only increase the design complexity somewhat, yet could prevent stress concentration in tension as well.

Additional improvements, as beautifully shown by Masoumi Khalil Abad et al. When loaded along the direction of the rigid ribs, the force-displacement curve closely matches that of the honeycomb characterized by Gibson et al.