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• W4233159279 abstract "physica status solidi (b)Volume 254, Issue 12 1770266 PrefaceFree Access Auxetics and Other Systems of Anomalous Characteristics First published: 11 December 2017 https://doi.org/10.1002/pssb.201770266Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Thirty years ago, in 1987, Lakes published his seminal paper on manufacturing foams with negative Poisson's ratio (NPR) 1. In the same year results of computer simulations of a simple molecular model (of two dimensional hard cyclic hexamers which interact through purely geometric interactions, infinite when any hexamers overlap and zero otherwise) were published which indicated that these molecules spontaneously form a thermodynamic phase of NPR 2. Rigorous analytic study of cyclic hexamers interacting through site–site n-inverse-power potential (which tends to the hard potential when n tends to infinity) has revealed the mechanism of NPR in that system 3. The present volume on materials and models with NPR, often referred to as auxetics 4, and other systems of anomalous (negative) characteristics is the twelfth focus issue of physica status solidi (b) on this subject 5. For this volume, 24 papers have been assembled. In the issue, they are ordered according to their article number. To mention first, three of the papers report on microscopic models of auxetics: The paper Negative in-plane Poisson's ratio for single layer black phosphorous: An atomistic simulation study by Ho, Ho, Park and Kim 6 examines the auxeticity of single layer black phosphorus and graphene through molecular statics simulations. In this work it is shown that black phosphorus exhibits an in-plane negative Poisson's ratio in the zigzag direction when the applied strain exceeds 0.018. This phenomenon is explained through an interplay between bond stretching and bond rotation with the latter mechanism being mostly dominant in the initial deformation steps. Furthermore, two papers present work on poly(phenylacetylene) networks. One of these, On the structural and mechanical properties of poly(phenylacetylene) truss-like hexagonal hierarchical nanonetworks by Grima-Cornish, Grima, and Evans 7, focuses on a novel class of truss-like hexagonal hierarchical nanostructures which benefit from the presence of larger pores that make them less stiff than their graphyne or graphdiyne fully substituted counterparts. Simulations performed on these systems, which can have a wide range of applications such as nanofiltration, also suggest that they have the potential to exhibit out of plane auxetic behavior at high stain. In the second paper on this topic, On the mechanical properties of graphyne, graphdiyne and other poly(phenylacetylene) networks by Degabriele, Grima-Cornish, Attard, Caruana-Gauci, Gatt, Evans, and Grima 8, a number of different planar poly(phenylacetylene) geometries and topologies, one of which has never been studied before, are explored with a view to comparing their Poisson's ratio and stiffness. This work has shown that such systems can be specifically designed to exhibit negative Poisson's ratio, and that their stiffness can be controlled in an independent manner from the Poisson's ratios. This means that through molecular design, these systems can be tailored to exhibit a particular set of mechanical properties. The following six papers concern macroscopic auxetic systems: A combination of Finite Element Modelling (FEM), 3D printing and compression testing is used to investigate the mechanical response of a 3D cellular structure having four-fold symmetry about the axial direction in the paper Three-dimensional stiff cellular structures with negative Poisson's ratio by Li, Ma, Dong, and Lakes 9. The structure comprises vertical and horizontal ribs, with the horizontal ribs attached to alternating cuboid surface indents on the vertical ribs. A parametric investigation demonstrates that Poisson's ratios ranging from slightly positive to as low as -0.958 can be achieved for significantly enhanced stiffness compared to previously reported re-entrant auxetic foam. Rueger, Li and Lakes in their paper Observation of Cosserat elastic effects in a tetragonal negative Poisson's ratio lattice 10 provide some significant insights into the existence of Cosserat elasticity effects in tetragonal NPR lattices. The Cosserat lengths of these configurations are measured experimentally using torsion and bending experiments on 3D printed lattices. Cosserat elasticity effects are clearly visible for small width samples, with bending ratios almost 100% higher than the continuum elasticity case for lattice beams with the smallest width. In the paper Microstructural Effects on the Poisson's Ratio of Star-Shaped Two-Dimensional Systems by Wang, Shen and Liao 11, FEM modelling is used to undertake an investigation into the effect of edge angle variations on the effective in-plane Poisson's ratio, Young's modulus and shear modulus responses of a 2D 4-pronged interconnected star honeycomb. Poisson's ratio is found to approach limiting values of +1 and −1 for the fully open and almost closed star units, respectively. An off-axis analysis is also performed and Poisson's ratio varies considerably more for the almost closed system than for the fully open structure. In the case of the former, the Poisson's ratio attains positive values for a range of off-axis values. The in-plane homogenised engineering constants of centersymmetric honeycombs with curved cells are detailed in the paper The elastic uniaxial properties of a center symmetric honeycomb with curved cell walls: effect of density and curvature by Harkati, Daoudi, Abaidia, and Bezazi 12 The paper introduces a series of analytical and Finite Element simulations to describe the uniaxial properties. The presence of curved cells walls appears to amplify the negative Poisson's ratio effect in classical ‘butterfly’ honeycomb configurations compared to their straight ligaments version. In their paper Tensile and Deformation Behavior of Auxetic Plied Yarns Ng and Hu 13 develop the double helix yarn concept to 4-ply and 6-ply yarn systems. The 4-ply system, comprising two centrally- located thick soft yarns with two thin stiff yarns spiraling around them, is investigated in detail and compared to the double helix yarn and 6-ply yarn. The 4-ply yarn is confirmed to be auxetic through tensile testing. By embedding samples under tension in epoxy, the authors identify outward movement of the soft yarns due to inward migration of the stiff yarns as the deformation mechanism responsible for the auxetic effect. Soft yarn diameter, stiff yarn modulus and twist level are found to be important factors in tailoring the Poisson's ratio response of the 4-ply yarn, which is found to persist over the entire strain range investigated (up to 25% applied strain). This contrasts with initially positive Poisson's ratio responses which transition to negative Poisson's ratio at intermediate strains for the double helix and 6-ply yarns. Analytical models for the prediction of Poisson's ratio and thermal expansion of a series of 2D and 3D arrays of connected ring structures are presented in the paper Analysis on an auxetic and negative thermal expansion structure based on interconnected array of rings and sliding rods by Lim 14. The paper is an exemplary demonstration of the interplay between structural elements, their connectivity and deformation on the effective mechanical and thermal properties. Various combinations of positive or negative Poisson's ratio with positive or negative thermal expansion are possible, depending on the choice of geometrical parameters. An interesting ‘sieve’ configuration is presented which possesses an overall zero coefficient of thermal expansion (to minimise thermal stresses) yet allows internal variation of pores upon change in temperature. Two papers discuss some applications of optimisation methods to the field of auxetics: Czarnecki and Lewiński in their paper Pareto optimal design of non-homogeneous isotropic material properties for the multiple loading conditions 15 perform the Pareto analysis of non-homogeneous isotropic material properties in bodies subjected to multiple loading conditions. The Pareto design is performed using two different techniques, and the reader can find in the paper a rigorous mathematical demonstration on how well-posed the related problems are. The particular test cases used in this work (pure traction problem and 3D cuboid clampedclamped rod) indicate that the presence of auxetic materials leads to stiffer structures, as identified by using these design approaches. The paper Computational simulation and optimisation of functionally graded auxetic structures made from inverted tetrapods by Novak, Vesenjak and Ren 16 describes an interesting 3D graded cellular configuration with auxetic characteristics that can be built by using additive layer manufacturing (ALM) techniques. The 3D cellular structures are produced by tessellated inverted tetrapods, which can generate several topologies, also in graded distribution. The authors provide a set of explicit nonlinear FEM simulations of the crushing performance, and clearly show that the optimised graded topology is able to generate a very controllable and smooth maximum reaction force during crushing, with a significant increase of the energy absorbed compared to the non-graded case. In a further seven papers, various continuous approaches to auxetics are presented: In the paper Two-layered tubes from cubic crystals. Auxetic tubes, Goldstein, Gorodtsov, Lisovenko, and Volkov 17 describe the homogenized Young's modulus and Poisson's ratio of two-layered tube systems made with different combinations of cubic crystals, auxetic or nonauxetic. The properties are derived within the framework of Saint-Venant approximations and curvilinear anisotropic elasticity. Quite significantly, the paper demonstrates that large negative Poisson's ratios are possible even when combinations of nonauxetic materials are used. In Torsion of a two-phased composite bar with helical distribution of constituents, Jopek and Strek 18 study the torsional characteristics of quasi-cylindrical bi-material composite bars having a pre-defined helical spatial distribution of materials, where the two materials can have different Poisson's ratios, one of which can be auxetic. Through use of FEM they show that both the mechanical properties, in particular the Poisson's ratio, and helical pitch have an influence on the torsional behaviour of the bar, including its elastic strain energy when subjected to torsion. Another paper by Strek's group, Finite element analysis of the influence of the covering auxetic layer of a plate on the contact pressure (Strek, Matuszewska, and Jopek) 19, looks into the effect of having a semi-cylinder bar pushing into a clamped auxetic plate or a conventional plate covered with an auxetic layer. It is shown, through a validated approach based on the augmented Lagrangian method, that the Poisson's ratio affects both the length of extent of the contact boundary as well as the contact pressure values. For example, for the homogeneous auxetic plate with Poisson's ratio tending to −1, there is an extensive decrease in the length of the contact boundary with an associated increase of contact pressure values. In his paper An accurate design equation for the maximum deflection of SSF sectorial plates made from auxetic materials Lim 20 explores the interlink between auxeticity and mechanics of plates and solids. He examines the relation between Poisson's ratio of isotropic 3D material systems and maximum deflection of sectorial plates with Simply-Supported straight edges and Free curve edge (SSF). The paper shows that the interplay between boundary conditions and auxeticity is important to define the global deformation mechanism of those plates: stiffening effects for negative Poisson's ratio materials do arise for SSF conditions, and quite interestingly the opposite when all the three edges are simply supported. Shear deformation in a class of thick hexagonal plates by Lim 21 concerns the shear correction factor for a simply supported and uniformly loaded regular hexagonal plate. Results of the investigations show that the shear deformation is suppressed if the plate material is auxetic. When benchmarked against other plate shapes, the shear deformation for the hexagonal plate is comparable with those of square and equilateral triangular plates. The response of a soft matrix containing a stiff thin embedded layer subject to cylindrical flat indentation is investigated using Finite Element Modelling in the paper The Effects of Poisson's Ratio on the Indentation Behaviour of Materials with Embedded System in an Elastic Matrix by Li, Al-Badani, Gu, Lake, Li, Rothwell, and Ren 22. Matrix Poisson's ratio is found to have a significant effect on the indentation stiffness of the system. A 30% increase in indentation stiffness is found for a thin inextensible shell near to, or on, the surface of an auxetic matrix. The maximum principal radial in-plane stress acting on the embedded layer is lower in magnitude when an auxetic matrix is employed. A compressive radial stress acts on the layer under the indenter in the case of an auxetic matrix, whereas a tensile stress is present for a positive Poisson's ratio matrix. This work is especially relevant to applications in the medical and sports engineering sectors which increasingly use soft materials with embedded stiff layers. Dyskin, Pasternak and Xu, in their paper Behaviour of extreme auxetic and incompressible elastic materials 23, investigate auxetic isotropic elastic materials with the Poisson's ratio of exactly −1 and isotropic materials with the Poisson's ratio close to 0.5 (incompressible). The analysis presented in the paper leads to the conclusion that deformation mechanisms in the studied extreme cases are qualitatively different. In particular, it is shown that the deformation of extreme auxetics can be uniform and should not be affected by fracture accumulation whereas nearly incompressible materials can show non-uniformity of deformation when the cracks are formed by tensile or simultaneous tensile and shear fracturing of the material. Two papers in this issue discuss engineering and practical applications of auxetics: The paper On the use of auxetics in footwear: Investigating the effect of padding and padding material on forefoot pressure in high heels by Stojmanovski-Mercieca, Formosa, Grima, Chockalingam, Gatt, and Gatt 24, attempts to investigate the effectiveness of auxetics in footware applications. Through a preliminary clinical study, they show that plantar covers fabricated from auxetic foams enable a better distributing of plantar pressure when high heels are used when compared to standard ones made from commercially available materials. In the paper Fabrication of auxetic foam sheets for sports applications, Allen, Hewage, Newton-Mann, Wang, Duncan, and Alderson 25, investigate techniques to fabricate large thin sheets of auxetic foam. The aim of the work is to facilitate future production and testing of prototype sports equipment utilising this material. A further paper concerns systems of negative compressibility: In his paper 2D Structures Exhibiting Negative Area Compressibility 26, Lim develops analytical expressions for the effective area compressibility of square and hexagonal arrays of deformable 2D 8-sided and 6-sided polygons, respectively. The polygons maintain constant edge length and are connected by rigid rods. It is shown that there exist ranges of characteristic edge angles where increasing in-plane pressure leads to an increase in the area of the interconnected polygon systems, corresponding to negative area compressibility for these systems. Negative Poisson's ratio behaviour is also expected for certain ranges of parameters of both systems. Finally, the volume contains three papers in which microscopic models of unusual behaviours are studied: Non-Equilibrium Molecular Dynamics (NEMD) simulations of confined sheared Lennard-Jones molecular films are presented by Maćkowiak, Heyes, Pieprzyk, Dini, and Brańka in their paper Non-Equilibrium Phase Behavior of Confined Molecular Films at Low Shear Rates 27. The NEMD equations of motion are consistent with the ‘soft spring’ limit of the Prandtl–Tomlinson model. Stick-slip behavior is found for pressures up to 1000 MPa. Anomalous friction behavior in the so-called Plug-Slip part of the non-equilibrium phase diagram is investigated. The study is expected to be significant for a molecularly thin lubricant material between two sliding surfaces in miniaturized MEMS devices, for example. In the article Nanowire stretching by Non-equilibrium Molecular Dynamics, Heyes, Dini, Smith, and Brańka 28 examine microstructural and mechanical properties of a stretched Lennard-Jones (LJ) model single crystal nanowire with square cross-section as a function of strain and strain rate. The instantaneous Poisson's ratio and Young's modulus are shown to be strongly strain dependent from the start of the pulling process. Finally, in the paper Maximum Poisson's ratios in planar isotropic crystals of binary hard discs at high pressures by Tretiakov, Bilski, and Wojciechowski 29, several isotropic two-dimensional crystalline model structures, formed by hard discs of two slightly different diameters, are studied by Monte Carlo simulations in the isobaric–isothermal ensemble with variable shape of the periodic box. Some of the structures are shown to exhibit maximum values of Poisson's ratio in the limit of very high pressures, i.e. when the particles are very close to each other. The revealed structures of maximum Poisson's ratios will constitute reference models in further studies which aim at understanding the maximum values of Poisson's ratio in a broad class of binary or polydisperse systems. We thank all the contributors of this thematic issue for submitting interesting papers. We are grateful to all the reviewers for valuable comments. Organizational efforts of Professor Jaroslaw Rybicki and Dr. Szymon Winczewski (both from Gdansk University of Technology, Poland), and Dr. Jakub W. Narojczyk (from Institute of Molecular Physics of the Polish Academy of Sciences, Poznan, Poland), without whom this volume would not contain some of the submissions, are also acknowledged. References 1 R. S. Lakes, Science 1987, 235(4792), 1038– 1040 2 K. W. Wojciechowski, Mol. Phys. 1987, 61(5), 1247– 1258 3 K. W. Wojciechowski, Phys. Lett. A 1989, 137(1-2), 60– 64 4 K. E. Evans, Endeavour, 1991, 15(4), 170– 174 5 K. W. Wojciechowski, F. Scarpa, J. N. Grima, A. Alderson, Phys. Status Solidi B, 2016, 253(7), 1241– 1242 6 D. T. Ho, V. H. Ho, H. S. Park, S. Y. Kim, Phys. Status Solidi B, 2017, 254, 1700285 (this issue). 7 J. N. Grima-Cornish, J. N. Grima, K. E. Evans, Phys. Status Solidi B, 2017, 254, 1700190 (this issue) 8 E. P. Degabriele, J. N. Grima-Cornish, D. Attard, R. Caruana-Gauci, R. Gatt, K. E. Evans, J. N. Grima, Phys. Status Solidi B, 2017, 254, 1700380 (this issue). 9 D. Li, J. Ma, L. Dong, R. S. Lakes, Phys. Status Solidi B, 2017, 254, 1600785 (this issue). 10 Z. Rueger, D. Li, R. S. Lakes, Phys. Status Solidi B, 2017, 254, 1600840 (this issue). 11 Y.-C. Wang, M.-W. Shen, S.-M. Liao, Phys. Status Solidi B, 2017, 254, 1700024 (this issue). 12 E. H. Harkati, N. E.-H. Daoudi, C. E. Abaidia, A. Bezazi, F. Scarpa, Phys. Status Solidi B, 2017, 254, 1600818 (this issue). 13 W. S. Ng, H. Hu, Phys. Status Solidi B, 2017, 254, 1600790 (this issue). 14 T.-C. Lim, Phys. Status Solidi B, 2017, 254, 1600775 15 S. Czarnecki, T. Lewiński, Phys. Status Solidi B, 2017, 254, 1600821 (this issue). 16 N. Novak, M. Vesenjak, Z. Ren, Phys. Status Solidi B, 2017, 254, 1600753 (this issue). 17 R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko, M. A. Volkov, Phys. Status Solidi B, 2017, 254, 1600815 (this issue). 18 H. Jopek, T. Strek, Phys. Status Solidi B, 2017, 254, 1700050 (this issue). 19 T. Strek, A. Matuszewska, H. Jopek, Phys. Status Solidi B, 2017, 254, 1700103 20 T.-C. Lim, Phys. Status Solidi B, 2017, 254, 1600784 (this issue). 21 T.-C. Lim, Phys. Status Solidi B, 2017, 254, 1700014 (this issue). 22 S. Li, K. Al-Badani, Y. Gu, M. Lake, L. Li, G. Rothwell, J. Ren, Phys. Status Solidi B, 2017, 254, 1600832 (this issue). 23 A. V. Dyskin, E. Pasternak, Y. Xu, Phys. Status Solidi B, 2017, 254, 1600851 (this issue). 24 L. A. Stojmanovski Mercieca, C. Formosa, J. N. Grima, N. Chockalingam, R. Gatt, A. Gatt, Phys. Status Solidi B, 2017, 254, 1700528 (this issue). 25 T. Allen, T. Hewage, C. Newton-Mann, W. Wang, O. Duncan, A. Alderson, Phys. Status Solidi B, 2017, 254, 1700596 (this issue). 26 T.-C. Lim, Phys. Status Solidi B, 2017, 254, 1600682 (this issue). 27 S. Maćkowiak, D. M. Heyes, S. Pieprzyk, D. Dini, A. C. Brańka, Phys. Status Solidi B, 2017, 254, 1600862 (this issue). 28 D. M. Heyes, D. Dini, E. R. Smith, A. C. Brańka, Phys. Status Solidi B, 2017, 254, 1600861 (this issue). 29 K. V. Tretiakov, M. Bilski, K. W. Wojciechowski, Phys. Status Solidi B, 2017, 254, 1700543 (this issue). Citing Literature Volume254, Issue12December 20171770266 ReferencesRelatedInformation" @default.
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