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A 2D metastable carbon allotrope, penta-graphene, composed entirely of carbon pentagons and resembling the Cairo pentagonal tiling, is proposed. State-of-the-art theoretical calculations confirm that the new carbon polymorph is not only dynamically and mechanically stable, but also can withstand temperatures as high as 1000 K. Due to its unique atomic configuration, penta-graphene has an unusual negative Poisson’s ratio and ultrahigh ideal strength that can even outperform graphene. Furthermore, unlike graphene that needs to be functionalized for opening a band gap, penta-graphene possesses an intrinsic quasi-direct band gap as large as 3.25 eV, close to that of ZnO and GaN. Equally important, penta-graphene can be exfoliated from T12-carbon. When rolled up, it can form pentagon-based nanotubes which are semiconducting, regardless of their chirality. When stacked in different patterns, stable 3D twin structures of T12-carbon are generated with band gaps even larger than that of T12-carbon. The versatility of penta-graphene and its derivatives are expected to have broad applications in nanoelectronics and nanomechanics. Significance Carbon has many faces––from diamond and graphite to graphene, nanotube, and fullerenes. Whereas hexagons are the primary building blocks of many of these materials, except for C ₂₀ fullerene, carbon structures made exclusively of pentagons are not known. Because many of the exotic properties of carbon are associated with their unique structures, some fundamental questions arise: Is it possible to have materials made exclusively of carbon pentagons and if so will they be stable and have unusual properties? Based on extensive analyses and simulations we show that penta-graphene, composed of only carbon pentagons and resembling Cairo pentagonal tiling, is dynamically, thermally, and mechanically stable. It exhibits negative Poisson's ratio, a large band gap, and an ultrahigh mechanical strength.

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson’s ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

In comparing a material's resistance to distort under mechanical load rather than to alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically. The numerical limits are set by ½ and −1, between which all stable isotropic materials are found. 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. Poisson's ratio describes the resistance of a material to distort under mechanical load rather than to alter in volume. On the bicentenary of the publication of Poisson's Traité de Mécanique , the continuing relevance of Poisson's ratio in the understanding of modern materials is reviewed.

Poisson effect is a phenomenon in the mechanics of geotechnical materials, which means that when a material is subjected to tension (or compression) in one direction, it will shrink (or expand) in the direction perpendicular to the tension (or compression) direction. This phenomenon of the correlation between lateral deformation and longitudinal deformation is called Poisson effect. Firstly, this paper analyzes the basic definition and range of Poisson’s ratio, including the homogeneous range at small strains. Secondly, it extends to the concept of negative Poisson’s ratio and the material structure of negative Poisson’s ratio. Then the determination method and value range of Poisson’s ratio in rock and soil were analyzed. For loose sand, Poisson’s ratio is usually between 0.2-0.4. For cohesive soils, the Poisson’s ratio may be higher, approximately between 0.3-0.5. The Poisson’s ratio of granite is usually between 0.2-0.3, while the Poisson’s ratio of shale may reach 0.3-0.4. This analysis is of great significance and guidance for a deeper understanding of the physical and mechanical properties of rock and soil masses, as well as for the stability analysis of geotechnical engineering.

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size ( d max / d min ) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios ( L / d ) were studied for each d max / d min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L / d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L / d , although the rate of increase decreases with larger L / d . This is mainly caused by the decrease of model porosity with larger L / d associated with the default PFC3D method and the better balanced contact force chains at larger L / d . After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L / d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L / d instead, and the average simulated Poisson’s ratio versus L / d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d max / d min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d max / d min . This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.

A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poisson's ratio (auxetic), zero Poisson's ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.

This paper presents a study of using weft-knitting technology to fabricate negative Poisson’s ratio (NPR) knitted fabrics, which exhibit the unusual property of becoming wider when stretched. Based on a geometrical analysis of a three-dimensional NPR structure constructed with parallelogram planes of the same shape and size, a new kind of NPR weft-knitted fabric was firstly designed and fabricated on a computerized flat-knitting machine. Then the NPR values of these fabrics were evaluated and compared with those from the theoretical calculations. The results show that all knitted fabrics have the NPR effect, which decreases with increased strain in the course direction. This variation trend is consistent with the theoretical prediction. The results also show that the main structure parameter affecting the NPR effect of a fabric is the opening angle at its initial state. Fabric with a smaller opening angle will have higher NPR values. This paper demonstrates the feasibility of fabricating NPR-knitted fabrics by using weft-knitting technology if a suitable structure and parameters are selected.

The development of auxetic materials, known for their unique negative Poisson’s ratio, is transforming various industries by introducing new mechanical properties and functionalities. These materials offer groundbreaking applications and improved performance in engineering and other areas. Initially found in natural materials, auxetic behaviors have been developed in synthetic materials. Auxetic materials boast improved mechanical properties, including synclastic behavior, variable permeability, indentation resistance, enhanced fracture toughness, superior energy absorption, and fatigue properties. This article provides a thorough review of auxetic materials, including classification and applications. It emphasizes the importance of cellular structure topology in enhancing mechanical performance and explores various auxetic configurations, including re-entrant honeycombs, chiral models, and rotating polygonal units in both two-dimensional and three-dimensional forms. The unique deformation mechanisms of these materials enable innovative applications in energy absorption, medicine, protective gear, textiles, sensors, actuating devices, and more. It also addresses challenges in research, such as practical implementation and durability assessment of auxetic structures, while showcasing their considerable promise for significant advancements in different engineering disciplines.

This paper presents an innovative three-dimensional (3D) fabric structure for composite reinforcement. Different from most conventional 3D fabric structures, the new structure displays a negative Poisson’s ratio (NPR) effect under compression. Based on a manufacturing process developed by combining both non-weaving and knitting technologies, four NPR 3D fabric samples with different warp yarn diameters were first manufactured manually. Then, their Poisson’s ratio (PR) values under compression along the fabric thickness direction were experimentally evaluated. A geometrical model was also proposed for the theoretical calculation of PR values of these fabrics and was compared with experimental data. The good agreements were obtained between the calculation and experiment. The results show that all the 3D fabrics display NPR effect under compression, which results in a unique feature that allows the structure to concentrate itself under the compressive load to better resist the load. This special feature makes this innovative 3D fabric structure very attractive for many potential applications such as automobile, aerospace, defense and sports equipment, where impact protection can be a highly desirable property.

Model lattices consisting of balls connected by central-force springs provide much of our understanding of mechanical response and phonon structure of real materials. Their stability depends critically on their coordination number z . d -dimensional lattices with z = 2 d are at the threshold of mechanical stability and are isostatic. Lattices with z < 2 d exhibit zero-frequency “floppy” modes that provide avenues for lattice collapse. The physics of systems as diverse as architectural structures, network glasses, randomly packed spheres, and biopolymer networks is strongly influenced by a nearby isostatic lattice. We explore elasticity and phonons of a special class of two-dimensional isostatic lattices constructed by distorting the kagome lattice. We show that the phonon structure of these lattices, characterized by vanishing bulk moduli and thus negative Poisson ratios (equivalently, auxetic elasticity), depends sensitively on boundary conditions and on the nature of the kagome distortions. We construct lattices that under free boundary conditions exhibit surface floppy modes only or a combination of both surface and bulk floppy modes; and we show that bulk floppy modes present under free boundary conditions are also present under periodic boundary conditions but that surface modes are not. In the long-wavelength limit, the elastic theory of all these lattices is a conformally invariant field theory with holographic properties (characteristics of the bulk are encoded on the sample boundary), and the surface waves are Rayleigh waves. We discuss our results in relation to recent work on jammed systems. Our results highlight the importance of network architecture in determining floppy-mode structure.