Young's and shear moduli and Poisson's ratio of polycrystalline solids consisting of 2D quadratic and 3D cubic randomly oriented grains of the same size and shape is studied. Considered polycrystals are initially unstrained. It is shown that for such polycrystals the division of the mechanical stability regions into areas of various auxeticity properties is different than for monocrystalline solids. In particular the regions of complete auxeticity enlarge.
We consider 2- and 3-dimensional cubic monocrystalline and polycrystalline materials. Expressions for Young's and shear moduli and Poisson's ratio are expressed in terms of eigenvalues of the stiffness tensor. Such a form is well suited for studying properties of these mechanical characteristics on sides of the stability triangles. For crystalline high-symmetry directions lines of vanishing Poisson's ratio are found. These lines demarcate regions of the stability triangle into areas of various auxeticity properties. The simplest model of polycrystalline 2D and 3D cubic materials is considered.…
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…
Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are completely auxetic, non-auxetic and auxetic. Particular attention is paid to 2D crystals of quadratic symmetry. All mechanically stable quadratic crystals are characterized by three parameters belonging to a prism with the stability triangle in the base. Regions in the stability triangle in which quadratic materials are completely auxetic, non-auxetic, and …
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…
A simple model is developed to predict the complex mechanical properties of carbon nanotube sheets (buckypaper) [Hall \textit{et al.}, \textit{Science} \textbf{320} 504 (2008)]. Fabricated using a similar method to that deployed for making writing paper, these buckypapers can have in-plane Poisson's ratios changed from positive to negative, becoming auxetic, as multiwalled carbon nanotubes are increasingly mixed with single-walled carbon nanotubes. Essential structural features of the buckypapers are incorporated into the model: isotropic in-plane mechanical properties, nanotubes preferentiall…
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$_{2}$ …
Explicit expressions for inverse of Young's modulus E, inverse of shear modulus G, and Poisson's ratio for cubic media are considered. All these characteristics of elastic media depend on three components of the compliance tensor S, and on direction cosines of mutually perpendicular vectors m and n with fourfold symmetry axes. These characteristics are studied for all mechanically stable cubic materials for vectors n belonging to the irreducible body angle subtended by three cubic high symmetry directions [001], [111], and [110]. Regions in the stability triangle of in which cubic elastic mate…
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…
"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).…
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…
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…
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…
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…
We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of linear and torsional springs, thus allowing the problem to be solved through a transfer matrix method. We show a non-trivial region of design space that yields materials with auxetic properties for strains greater than that required to trigger elastic instability. The critical loading required to make this transition from positive to negative Poisson's ratio is…
Membranes of carbon allotropes comprised solely of densely packed pentagonal rings, known as pentagraphene, exhibit negative Poisson's ratio (auxetic behavior) and a bandgap of $3.2$ eV. In this work, we investigated the structural stability, mechanical and fracture properties of nanotubes formed by rolling up pentagraphene membranes, the so-called pentagraphene nanotubes (PGNTs). Single-walled PGNT of three distinct configurations: zigzag, $α$-armchair, and $β$-armchair were studied combining first-principles calculations and reactive molecular dynamics simulations. Our results showed Young's…
We propose a Ginzburg-Landau theory for the elastic properties of shape memory polycrystals. A single crystal elastic free energy for a system that undergoes a square-to-rectangle transformation is generalized to a polycrystal by introducing a crystal orientational field that is determined from a continuum phase field model. The coupled system is used to study domain morphology and mechanical properties of shape memory alloys in different temperature regimes.
Different methods of texturing polycrystalline materials are developed over years to use/probe anisotropic material properties with relative ease, where complicated and expensive single crystal growth processes could be avoided. In this paper, particle morphology assisted texturing in multiferroic MnWO$_4$ has been discussed. Detailed powder x-ray diffraction vis-a-vis scanning electron microscopic studies on differently annealed and processed samples have been employed to probe the giant texturing effect in powdered MnWO$_4$. A quantitative measure of the texturing has been carried out by mea…
Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,…
The transport properties of highly oriented pyrolitic graphite (HOPG) and polycrystal graphite have been studied. The electric conductivity of HOPG is several times larger than that of the polycrystal graphite. Along with the large magnetoresistances (MR), the polycrystal graphite show the accordant semiconductor-like character in a wide temperature (roughly range from 20K to 120K) under 0, 4, 8, 12 T applied magnetic field, while the magnetic-field-induced metal-semiconductor-like transition was only found in HOPG. The difference of transport properties originates from the Coulomb interaction…
The mechanical properties of $β$-Sn single crystals have been systematically investigated using a combined methodology of micropillar tests and rate-dependent crystal plasticity modelling. The slip strength and rate sensitivity of several key slip systems within $β$-Sn single crystals have been determined. Consistency between the numerically predicted and experimentally observed slip traces has been shown for pillars oriented to activate single and double slip. Subsequently, the temperature-dependent, intermetallic-size-governing behaviour of a polycrystal $β$-Sn-rich alloy SAC305 (96.5Sn-3Ag-…
Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory for averaging the coefficients of the corresponding tensors unifying Voigt's, Reuss' or other self-consistent homogenization theories. We apply the method to determine elastic moduli of untextured polycrystals with arbitrary crystal structures, recovering experimental data with high precision for cubic materials. We show that the average moduli can be used t…
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 investigate the scaling properties of the Barkhausen effect, recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents τ= 1.50 \pm 0.05 or τ= 1.27 \pm 0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff o…
