Auxetic materials, or negative-Poisson's-ratio materials, are important technologically and fascinating theoretically. When loaded by external stresses, their internal strains are governed by correlated motion of internal structural degrees of freedom. The modelling of such materials is mainly based on ordered structures, despite existence of auxetic behaviour in disordered structures and the advantage in manufacturing disordered structures for most applications. We describe here a first-principles expression for strains in disordered such materials, based on insight from a family of 'iso-auxetic' structures. These are structures, consisting of internal structural elements, which we name 'auxetons', whose inter-element forces can be computed from statics alone. Iso-auxetic structures make it possible not only to identify the mechanisms that give rise to auxeticity, but also to write down the explicit dependence of the strain rate on the local structure, which is valid to all auxetic materials. It is argued that stresses give rise to strains via two mechanisms: auxeton rotations and auxeton expansion / contraction. The former depends on the stress via a local fabric tensor, which we define explicitly for 2D systems. The latter depends on the stress via an expansion tensor. Whether a material exhibits auxetic behaviour or not depends on the interplay between these two fields. This description has two major advantages: it applies to any auxeton-based system, however disordered, and it goes beyond conventional elasticity theory, providing an explicit expression for general auxetic strains and outlining the relevant equations.
The use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a first order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various p…
Auxetic materials (materials with negative Poisson's ratio) and nanomaterials have independently been for many years two of the most active research fields in material science. Recently, these formerly independent fields have begun to intersect in new and interesting ways due to the recent discovery of auxeticity in nanomaterials like graphene, metal nanoplates, black phosphorus, and others. Here we review the research emerging at the intersection of auxeticity and nanomaterials. We first survey the atomistic mechanisms, both intrinsic and extrinsic, that have been found, primarily through ato…
Mechanically reconfigurable reflectors can modify their geometries to realize large angle beam scanning. This paper studies a method for reconfiguring a reflector geometry from a standard parabolic shape to offset parabolic shapes with varies offset angles. To fulfil the geometry control, the coordinate change of the nodes on the reflector surface are studied with the coordinate transformation method. To accommodate the large deformation of the reflector surface, a negative Poisson's ratio (NPR) material is applied to the reconfigurable reflector.
By means of extensive ab initio calculations, a new two-dimensional (2D) atomic material tin selenide monolayer (coined as tinselenidene) is predicted to be a semiconductor with an indirect gap (1.45 eV) and a high hole mobility (of order 10000 cm2V-1S-1), and will bear an indirect-direct gap transition under a rather low strain (<0.5 GPa). Tinselenidene has a very small Young's modulus (20-40 GPa) and an ultralow lattice thermal conductivity (<3 Wm-1K-1 at 300 K), making it probably the most flexible and most heat-insulating material in known 2D atomic materials. In addition, tinseleniden has…
Auxetic materials are of great engineering interest not only because of their fascinating negative Poisson's ratio, but also due to their increased toughness and indentation resistance. These materials are typically synthesized polyester foams with a very heterogeneous structure, but the role of disorder in auxetic behavior is not fully understood. Here, we provide a systematic theoretical and experimental investigation in to the effect of disorder on the mechanical properties of a paradigmatic auxetic lattice with a re-entrant hexagonal geometry. We show that disorder has a marginal effect on…
"Auxetic" materials have the counter-intuitive property of expanding rather than contracting perpendicular to an applied stretch, formally they have negative Poisson's Ratios (PRs).[1,2] This results in properties such as enhanced energy absorption and indentation resistance, which means that auxetics have potential for applications in areas from aerospace to biomedical industries.[3,4] Existing synthetic auxetics are all created by carefully structuring porous geometries from positive PR materials. Crucially, their geometry causes the auxeticity.[3,4] The necessary porosity weakens the materi…
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).…
We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry Π+ cylinder packing, transforming the cylinders themselves to the elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local re-entrant geometry at its vertices, and is shown to be auxetic when modelled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the tensegrity structure is subsequently modelled as a lattice material with elastic elements, …
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…
Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe bidimensional perfect auxetics with potential use in the design of new materials. Perfect auxetics are characterized by a Poisson's ratio $ν=-1$ over a finite strain range and can be modeled as materials composed of rotating rigid units. Inspired by a natural connection between these rotating rigid units with an antiferromagnetic spin system, here are unveiled th…
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…
Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachir…
In this work, we propose a new auxetic (negative Poisson's ratio values) structure, based on a $γ$-graphyne structure, here named $AγG$ $structure$. Graphynes are 2D carbon allotropes with phenylic rings connected by acetylenic groups. The A$γ$G structural/mechanical and electronic properties, as well as its thermal stability, were investigated using classical reactive and quantum molecular dynamics simulations. We found that A$γ$G has a large bandgap of 2.48 eV and is thermally stable at a large range of temperatures. It presents a Young's modulus that is an order of magnitude smaller than th…
Structural-property relationship, the connection between materials' structures and their properties, is central to the materials research. Especially at reduced dimensions, novel structural motifs often generate unique physical properties.Motivated by a recent work reporting a novel half auxetic effect in monolayer PdB4 with a hypercoordinated structure, here, we extensively explore similar 2D transition metal boride structures MB4 with M covering 3d and 4d elements.Our investigation screens out one stable candidate, the monolayer RhB4. We find that monolayer RhB4 also shows half auxeticity, i…
Tetrahex-carbon is a recently predicted two dimensional (2D) carbon allotrope which is composed of tetragonal and hexagonal rings. Unlike flat graphene, this new 2D carbon structure is buckled, possesses a direct band gap ~ 2.6 eV and high carrier mobility with anisotropic feature. In this work, we employ first-principles density-functional theory calculations to explore mechanical properties of tetrahex-C under uniaxial tensile strain. We find that tetrahex-C demonstrates ultrahigh ideal strength, outperforming both graphene and penta-graphene. It shows superior ductility and sustains uniaxia…
The existence of a new two dimensional CN2 structure was predicted using ab-initio molecular dynamics (AIMD) and density-functional theory calculations. It consists tetragonal and hexagonal rings with C-N and N-N bonds arranged in a buckling plane, isostructural to tetrahex-carbon allotrope. It is thermodynamically and kinetically stable suggested by its phonon spectrum and AIMD. This nanosheet has high concentration of N and contains N-N single bonds with an energy density of 6.3 kJ/g, indicating potential applications as high energy density materials. It possesses exotic mechanical propertie…
最近的推导[P. H. Mott和C. M. Roland，Phys.Rev.B80，132104（2009）.]对线弹性材料泊松比v的界限的研究表明，传统的下限-1是错误的，经典弹性理论的有效值v不能小于0.2。这是一个重要的结果，因为对于具有小的v值的材料，直接测量是不可行的，因此必须从其他弹性常数计算v。在这里，我们直接测量泊松比的四种材料，其中两个更严格的限制范围v适用，和两个值低于此限制的0.2。我们发现，虽然前者的测量值v相当于从剪切和拉伸模量计算的值，对于两种拉胀材料（v < 0），经典弹性方程给出了不准确的v值。这是实验证实，泊松比的正确下限是0.2，以经典弹性适用。
In this paper, we perform theoretical study on the physical properties of two-dimensional transition metal chalcogenides MX$_{2}$ and M$_{2}$X$_{3}$ (M= Ni, Pd; X= S, Se, Te). These studied materials are classified in three stable phases according to their lattice structures: hexagonal MX$_{2}$, orthorhombic MX$_{2}$ and orthorhombic M$_{2}$X$_{3}$. They have either isotropic or anisotropic in-plane properties depending on their symmetries. In particular, the orthorhombic MX$_{2}$ and M$_{2}$X$_{3}$ have low lattice symmetry and present highly anisotropic properties. The orthorhombic MX$_{2}$ …
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…
The bi-alkali pnictogens have attracted significant attention for optoelectronic and photocathodic device applications. However, in most of the compounds belonging to this family, there has been less effort put into investigating the mechanical properties and topological phase transitions (TPT) of the compounds. Here, in the framework of density functional theory, the mechanical properties and topological phase transition of NaLi$_{2}$Bi under hydrostatic pressures are investigated. Elastic constants and phonon calculations have shown the mechanical and dynamical stability of this compound und…
The ability to measure small deformations or strains is useful for understanding many aspects of materials. Here, a new analysis of speckle diffraction peaks is presented in which the systematic shifts of the speckles are analyzed allowing for strain (or flow) patterns to be inferred. This speckle tracking technique measures strain patterns with a accuracy similar to x-ray single crystal measurements but in amorphous or highly disordered materials.
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 influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield strength model is proposed. The model accounts for random variations in particle size and elastic properties, and is numerically validated against FE solutions in 2D/3D material cell models. Excellent agreement is found as long as the typical particle radius is much smaller than the material length scale, given that the particle volume fraction is not too large…
A 3D unit cell model containing eight different spherical particles embedded in a homogeneous strain gradient plasticity (SGP) matrix material is presented. The interaction between particles and matrix is controlled by an interface model formulated within the higher order SGP theory used. Strengthening of the particle reinforced material is investigated in terms of the increase in macroscopic yield stress. The results are used to validate a closed form strengthening relation proposed by the authors, which suggests that the increase in macroscopic yield stress is governed by the interface stren…
In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notched aluminium alloy specimen loaded in cyclic tension. The model is based on an objective representation of the deformation and stress measures and on a rate type constitutive equations. It does not only complies with the principles of material model…
Transformer-based prediction of two-dimensional material electronic properties under elastic strain engineering
School of Materials Science and Engineering, Beijing Institute of Technology（北京理工大学材料学院）；School of Chemistry and Chemical Engineering, Beijing Institute of Technology（北京理工大学化学与化学工程学院）
Reconfigurable Strain Gradient Polarity in Crystalline Oxide Nanomembranes for Controlled Bending of Functional Materials
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Physics, Stanford University（斯坦福大学物理系）
The mechanical response of isotropic elastoplastic materials containing random distributions of initially spherical voids is investigated computationally based on Fast Fourier Transform simulations. Numerical limit-analysis simulations at constant stress triaxiality allow to determine the yield surfaces, leading in particular to the determination of a Representative Volume Element size for the onset of coalescence / inhomogeneous yielding. Moreover, two different coalescence regimes are observed that differ by the presence of shearing. The yield surfaces are found to be consistent with the com…
Integrating layered two-dimensional (2D) materials into 3D heterostructures offers opportunities for novel material functionalities and applications in electronics and photonics. In order to build the highest quality heterostructures, it is crucial to preserve the cleanliness and morphology of 2D material surfaces that come in contact with polymers such as PDMS during transfer. Here we report that substantial residues and up to ~0.22% compressive strain can be present in monolayer MoS$_{2}$ flakes transferred using PDMS. We show that a UV-ozone pre-cleaning of the PDMS surface before exfoliati…
Herein, we demonstrate that first-principles calculations can be used for mapping electronic properties of two-dimensional (2d) materials with respect to non-uniform strain. By investigating four representative single-layer 2d compounds with different symmetries and bonding characters, namely 2d-${MoS_2}$, phosphorene, $α$-Te, and $β$-Te, we reveal that such a mapping can be an effective guidance for advanced strain engineering and development of strain-tunable nanoelectronics devices, including transistors, sensors, and photodetectors. Thus, we show that $α$-Te and $β$-Te are considerably mor…
This work presents an automated three-point bending apparatus that can be used to study strain engineering and straintronics in two-dimensional materials. We benchmark the system by reporting reproducible strain tuned micro-reflectance, Raman, and photoluminescence spectra for monolayer molybdenum disulfide (MoS2). These results are in good agreement with reported literature using conventional bending apparatus. We further utilize the system to automate strain investigations of straintronic devices by measuring the piezoresistive effect and the strain effect on photoresponse in an MoS2 electri…
A Robust "Shrink-and-wrap" Piecewise Construction Transforms 3-Dimensional Mesh Structures into Mechanical Metamaterials
Stony Brook University, the State University of New York (SUNY)（纽约州立大学石溪分校）；Department of Biomedical Engineering（纽约州立大学石溪分校工程与应用科学学院）；College of Engineering and Applied Sciences (CEAS)；Stony Brook University, SUNY
We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on the concomitant strain localization process (formation of a macroscopic shear band). It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress-strain curves. The evolving strain localization patterns are characterize…
We present electrothermal microelectromechanical (MEMS) actuators as a practical platform for straining 2D materials. The advantages of the electrothermal actuator is its high output force and displacement for low input voltage, but its drawback is that it is actuated by generating high amounts of heat. It is crucial to mitigate the high temperatures generated during actuation for reliable 2D material strain device implementation. Here, we implement a chevron actuator design that incorporates a thermal isolation stage in order to avoid heating the 2D material from the high temperatures generat…
Hexagonal boron nitride is an indirect band gap material with a strong luminescence in the ultraviolet. This luminescence originates from bound excitons recombination assisted by different phonon modes. The coupling between excitons and phonons is so strong that the resulting light emission is as efficient as the one of direct band gap materials. In this manuscript we investigate how uniaxial strain modifies the electronic and optical properties of this material, and in particular how it affects the exciton-phonon coupling. Using a formulation of this coupling based on finite-difference displa…
