We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.
Cork is a natural amorphous material with near-zero Poisson's ratio that is ubiquitously used for sealing glass bottles. It is an anisotropic, transversally isotropic, composite that can hardly be scaled down. Here, we propose a new class of isotropic and reusable cork-like metamaterial that is designed from an hybrid truss-lattice material to show an isotropic Poisson's ratio close to zero. Optimization is conducted using a multi-objective genetic algorithm, assisted by an elliptical basis function neural network, and coupled with finite element simulations. The optimal micro-structured metam…
A long-standing question is why Poisson's ratio v nearly always exceeds 0.2 for isotropic materials, whereas classical elasticity predicts v to be between -1 to 1/2. We show that the roots of quadratic relations from classical elasticity divide v into three possible ranges: -1 < v <= 0, 0 <= v <= 1/5, and 1/5 <= v < 1/2. Since elastic properties are unique there can be only one valid set of roots, which must be 1/5 <= v < 1/2 for consistency with the behavior of real materials. Materials with Poisson's ratio outside of this range are rare, and tend to be either very hard (e.g., diamond, beryll…
The lower bound usually cited for Poisson's ratio ν is -1, derived from the relationship between ν and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ν for isotropic materials is actually 1/5, a value also consistent with experimental measurements on real materials. Herein we generalize this result, first by analyzing expressions for ν in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate the prior finding that 1/5 <= ν for linear elasticity to be applica…
We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well known in material systems with directional interactions (e.g., zirconium tungstate), to our kn…
electromagnetic field distributions are found for frequencies slightly under one hundred giga Hertz, using a left handed substrate in a microstrip guided wave structure
A material exhibiting a negative Poisson's ratio is always one of the leading topics in materials science, which is due to the potential applications in those special areas such as defence and medicine. In this letter, we demonstrate a new material, few-layer orthorhombic arsenic, also possesses the negative Poisson's ratio. For monolayer arsenic, the negative Poisson's ratio is predicted to be around -0.09, originated from the hinge-like structure within the single layer of arsenic. When the layer increases, the negative Poisson's ratio becomes more negative and finally approaches the limit a…
We perform molecular dynamics simulations to investigate the effect of hydrogenation on the Poisson's ratio of graphene. It is found that the value for Poisson's ratio in graphene can be effectively tuned from positive to negative by varying the percentage of hydrogenation. Specifically, the Poisson's ratio decreases with the increase of the percentage of hydrogenation, and reaches a minimum value of -0.04 at the percentage of hydrogenation about 50%. The Poisson's ratio starts to increase with a further increase of the percentage of hydrogenation. The appearance of minimum negative Poisson's …
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve negative thermal expansion via a metamaterial approach. The metamaterial is constructed with unit cells that combine bi-material strips and anti-chiral structures. Both experimental and simulation results display isotropic negative thermal expansion properties. The coefficient of negative thermal expansion of the metamaterials is d…
The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. While 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. In the present work, we report using first principles calculations the existence of a negative Poisson's ratio in a single-layer, two-dimensional material, black…
The properties of artificial isotropic microwave composites which would possess simultaneously negative permittivity and permeability are studied theoretically. Four kinds of composites are considered. Two of them concern media with split-ring resonator particles with different particle arrangements. The other two are realized with Omega particles. An analytical antenna model of the electromagnetic behavior of a split-ring resonator (SRR) is suggested and verified by numerical simulations. Next, material parameters of composite media made with SRR or Omega particles are calculated. It is shown…
We report a three-dimensional mechanical metamaterial that simultaneously possesses negative stiffness, negative bulk modulus, and negative Poisson's ratio. This metamaterial is a periodic arrangement of binder-shell elements. Under compression, the spherical shells dent inwards which cause the material to contract in the lateral directions. At larger deformations, snap through instability occurs and the material exhibits negative incremental stiffness. Interestingly, both incremental stiffness and incremental Poisson's ratio approach negative infinity (under displacement control) when snap-ba…
The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus, and that our experimental observations are consistent with first principles simulations. Through ap…
Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In this work, we report that single-layer graphene exhibits an intrinsic NPR, which is robust and independent of its size and temperature. The NPR arises due to the interplay between two intrinsic deformation pathways (one with positive Poisson's ratio, the other with NPR), which correspond to the bond stretching and angle bending interactions in graphene. We prop…
The Poisson's ratio characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Though negative Poisson's ratios (NPR) are theoretically possible within continuum elasticity, they are most frequently observed in engineered materials and structures, as they are not intrinsic to many materials. In this work, we report NPR in single-layer graphene ribbons, which results from the compressive edge stress induced warping of the edges. The effect is robust, as the NPR is observed for graphene ribbons with widths smaller than about 10 nm, and for tensile …
Materials with a negative Poisson's ratio, also known as auxetic materials, exhibit unusual and counterintuitive mechanical behavior - becoming fatter in cross-section when stretched. Such behavior is mostly attributed to some special reentrant or hinged geometric structures regardless the chemical composition and electronic structure of a material. Here, using first principles calculations, we report a new class of auxetic single-layer two-dimensional (2D) materials, i.e., the 1T-type monolayer crystals of groups 6-7 transition-metal dichalcogenides, MX$_2$ (M = Mo, W, Tc, Re; X = S, Se, Te).…
The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the lon…
Silicon dioxide or silica, normally existing in various bulk crystalline and amorphous forms, is recently found to possess a two-dimensional structure. In this work, we use ab initio calculation and evolutionary algorithm to unveil three new 2D silica structures whose themal, dynamical and mechanical stabilities are compared with many typical bulk silica. In particular, we find that all these three 2D silica have large in-plane negative Poisson's ratios with the largest one being double of penta-graphene and three times of borophenes. The negative Poisson's ratio originates from the interplay …
This paper presents an auxetic medium, consisting of a two-dimensional perforated sheet where the holes are arranged in a repetitive pattern. The hexagonal disposition of the perforations makes the medium isotropic in the plane. It is shown that negative values of the Poisson's ratio can be achieved for specific values of the dimensions and orientations of the holes. The results of the numerical simulations are confirmed by experimental tests, in which the Poisson's ratio of each specimen examined is evaluated from the displacement field obtained from the Digital Image Correlation (DIC) techni…
We investigate three-dimensional left-handed and related meta-materials based on a fully symmetric multi-gap single-ring SRR design and crossing continuous wires. We demonstrate isotropic transmission properties of a SRR-only meta-material and the corresponding left-handed material which possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity. Minor deviations from complete isotropy are due to the finite thickness of the meta-material.
As a basic mechanical parameter, Poisson's ratio (ν) measures the mechanical responses of solids against external loads. In rare cases, materials have a negative Poisson's ratio (NPR), and present an interesting auxetic effect. That is, when a material is stretched in one direction, it will expand in the perpendicular direction. To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable. In this work, based on first principles calculations, we rediscover the previously proposed δ-phosphorene (δ-P) nanosheets [Jie Gua…
Auxetic behavior quantified by the negative Poisson's ratio (NPR) is commonly attributed to geometry evolution with re-entrant mechanism or other mechanical factors, which is thought to be independent of electronic structures. Thus, searching for electronic effect dominated auxetic behavior is challenging. Herein, from state-of-the-art first-principles calculations, by studying a class of two-dimensional (2D) transition metal chalcogenides (TMCs), namely X2Y2-type (X=Cu, Ag, Au; Y=O, S, Se) rectangular TMCs (R-TMCs), we identify that the monolayer R-Cu2Se2 unconventionally demonstrates a struc…
The in-plane infinitesimal deformations of graphene are well understood: they can be computed by solving the equilibrium problem for a sheet of isotropic elastic material with suitable stretching stiffness and Poisson coefficient $ν^{(m)}$. Here, we pose the following question: does the Poisson coefficient $ν^{(m)}$ affect the response to bending of graphene? Despite what happens if one adopts classical structural models, it does not. In this letter we show that a new material property, conceptually and quantitatively different from $ν^{(m)}$, has to be introduced. We term this new parameter b…
Transition metal carbides include a wide variety of materials with attractive properties that are suitable for numerous and diverse applications. Most recent experimental advance could provide a path toward successful synthesis of large-area and high-quality ultrathin Mo2C membranes with superconducting properties. In the present study, we used first-principles density functional theory calculations to explore the mechanical and optical response of single-layer and free-standing Mo2C. Uniaxial tensile simulations along the armchair and zigzag directions were conducted and we found that while t…
Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we calculate the phonon band structures. On this basis, using cubic symmetry, we can unambiguously retrieve all different non-zero elements of the rank-4 effective metamaterial elasticity tensor, from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed b…
Based on variable components global optimization algorithm, we predict a stable two-dimensional (2D) phase of boron phosphide with 1:5 stoichiometry, i.e. boron pentaphosphide (BP_5) monolayer, which has a lower formation energy than that of the commonly believed graphitic phase (g-BP). BP_5 monolayer is a multiferroic material with coupled ferroelasticity and ferroelectricity. The predicted reversible strain is up to 41.41%, which is the largest among all reported ferroelastic materials. Due to the non-centrosymmetric structure and electronegativity differences between boron and phosphorus at…
Negative Poisson's ratio (NPR) materials have attracted tremendous interest due to their unusual physical properties and potential applications. Certain two-dimensional (2D) monolayer materials have also been found to exhibit NPR and the corresponding deformation mechanism varies. In this study, we found, based on first-principles calculations, that the Poisson's ratio (PR) sign of monolayer Blue Phosphorus Oxide (BPO) can be tuned by strain: the PR is positive under uniaxial strain <= -1% but becomes negative under > 0. The deformation mechanism for BPO under strain depends on the mutual comp…
School of Civil Engineering and Architecture, Wuhan University of Technology（武汉理工大学土木工程与建筑学院）；Sanya Science and Education Innovation Park of Wuhan University of Technology（武汉理工大学三亚科教创新园）
Using bases of fourth rank tensorial bases of complete Voigt's symmetry elaborated by Walpole we obtained expressions for inverse of Young's modulus E, inverse of shear modulus G and Poisson's ratio, which depend on components of the stiffness tensor S, on direction cosines of vectors n of uniaxial load and the vector m of lateral strain with crystalline symmetry axes. Crystalline media of high and medium symmetries are considered. Such representation yields decomposition of the above elastic characteristics to isotropic and anisotropic parts. Expressions for Poisson's coefficient are well sui…
