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The objective of this research is to understand more fully the out-of-plane auxetic behavior of paper. In the reported research, initial characterization of the auxetic properties of common, commercially available papers is described. The results of these experiments suggest that the auxetic response seen in paper structures is related to the cellulose fiber network structure, as previously suggested, and is related to inter-fiber bonding and fiber organization in the sheet. These results also indicate that further study is needed to understand how materials and processing variables influence auxetic behavior. A mathematical model, attempting to explain auxetic response in an idealized arrangement of fibers is included. Ultimately, the fundamental understanding resulting from this research should lead to new product development opportunities for forest product-based paper materials as well as to the establishment of predictive structure-property relations for auxetic materials using paper as a model system. [ABSTRACT FROM AUTHOR]

This is the fifteenth volume of I Physica Status Solidi B i focussed on materials and models showing negative Poisson's ratio (PR), which are often called auxetics, and other systems of unusual, e.g., "negative", characteristics. SP [ sp [1] SP ] sp This time it contains 19 papers which are grouped into three sections. This non-classical effect cannot occur in classical thermo-elasticity but is allowable in Cosserat solids. SP [ sp [17] SP ] sp Next, I Elena Pasternak and Arcady Dyskin i propose a mechanism to control the constriction of elastic rod modulus by lateral compression. This, amongst other things, opens a way to design materials ensuring vibration isolation. SP [ sp [18] SP ] sp I Haifeng Ruan and Dong Li i propose a hierarchical acoustic metamaterial with a spider-web-like structure. [Extracted from the article]

In this paper, the dynamic behavior of a three-layered sandwich beam with a metal foam core is investigated. Outer layers of the sandwich beam are made of AlSi12 alloy and the core is metal porous foam made of AlSi12. Numerical analysis is made for different parameters of the core -- average damping loss factor, densities, Young modulus, and Poisson's ratio of core foam. The simulations are used to determine the mechanical impedance for a sandwich beam with the applied harmonic load. Numerical calculations are made with the use of finite element method. The results imply that the auxetic core of the composite beam can have a great impact on the dynamic behavior (mobility) of the system. Furthermore, it appears that there are ranges of frequencies in which the mobility of the system can be minimized by using the auxetic foam core. [ABSTRACT FROM AUTHOR]

This paper reports a development of bi-stretch auxetic woven fabrics by using non-auxetic yarns and weaving technology. The fabric structure is first designed based on a re-entrant hexagonal geometry by combination of loose weave and tight weave in a woven fabric structure, and then fabricated on a rapier weaving machine by using both non-elastic and elastic yarns. Two variations of the fabric are produced by using different elastic yarn arrangement in weft direction. The designed auxetic geometry is finally achieved after a washing process due to creation of non-uniform contraction or shrinkage profiles within the fabric structural unit cell. The testing results showed that the developed fabrics exhibit negative Poisson ratio effect in both weft and warp directions in a large range of tensile strain. [ABSTRACT FROM AUTHOR]

This paper reports a new type of auxetic yarn made with circular braiding technology to overcome the yarn slippage problem in the conventional helical auxetic yarn structure. Various auxetic yarn structures are firstly produced on a vertical circular braiding machine with 16 yarn carries by changing the number and arrangement of stiff yarn as well as diameter of elastic yarn and core yarn, and then tested under single and repeating tensile conditions. The results show that not only yarn slippage problem could be overcome in the newly developed auxetic yarn structure, but also an early activation and a higher magnitude of negative Poisson's ratio could be achieved. The results also show that all structural parameters including stiff yarn number and arrangement, core yarn, and elastic yarn diameter have an influence on the auxetic effect of the novel yarn structure. Since the new auxetic yarn is produced by using standard braiding manufacturing technique and conventional non-auxetic yarns, there are few technological barriers for its largescale manufacture for practical application. [ABSTRACT FROM AUTHOR]

This work describes the identification of the shear modulus of open cell polyurethane thermoformed auxetic foams from 3- and 4-point bending tests. The foams are incorporated in sandwich beams with carbon fibre/epoxy face skins, and benchmarked against similar sandwich structures made with the conventional counterpart open cell foam. Three types of beams are tested: one with auxetic foams, another type related to a conventional foam core with the same thickness of the auxetic porous materials, and a third type of beam consisting in conventional foam with a thickness corresponding to an iso-weight configuration to the auxetic specimen. The auxetic foam has a shear modulus 7% lower than the one of the bulk conventional specimens, but higher shear stresses at large deformations and a smoother strain stiffening response compared to the beams with the conventional thinner core. The paper also highlights the low shear wave speed of these auxetic foams compared to other porous polymers used in helmet and head protection applications, as well as potential uses of the quasi-zero-stiffness behavior here observed for the auxetic foam sandwich beam. [ABSTRACT FROM AUTHOR]

The paper discusses the problem of recovery of the microstructure of the least compliant bodies of non-homogeneous optimal isotropic properties predicted by the Isotropic Material Design method. The three-dimensional microstructure is assumed as constructed by a subsequent lamination process in which two isotropic materials of ordered properties are used, the process being repeated three or six times, subsequently. The Hooke tensors closest to the optimal ones are found by making use of the analytical Francfort--Murat formulae for effective moduli of third and sixth rank sequential laminates. The ability to model an auxetic behavior within the subdomains where the optimal Poisson's ratio assumes negative values is also shown. [ABSTRACT FROM AUTHOR]

The paper moves from a technological process developed in previous works to produce chiral honeycombs made of thin composite laminates. Such approach is applied in this work to manufacture the morphing ribs for a variable camber wing-box. The specifications for such components are obtained by developing a finite element model of a demonstrator, which is designed taking into account aeroelastic performances, structural, and technological issues. In the first part of the paper, the design of such a demonstrator is presented and the role of composite chiral ribs with auxetic behavior is outlined. Production, testing, and numerical studies of manufacturing trials are performed to assess the technological process applied to small-sized chiral units made of different materials, to investigate their mechanical properties, and to validate a numerical approach for design and analysis. A complete chiral composite rib is then produced and tests are carried out to verify the overall structural response and to validate the numerical approach. [ABSTRACT FROM AUTHOR]

Helical arrangements are very common both in nature and in artificial structures. In this paper, an analysis of a prismatic composite bar is presented. The cross-sectional shape of the bar is described by a regular polygon. The composite is built of two homogeneous isotropic materials characterised by different Poisson's ratios one of which can be negative. Spatial distribution of materials in the composite is based on helical shape. Both materials are connected with the use of a transition zone of assumed width. The bar is subjected to torsional loading and its behavior is investigated by means of FEM method. Both material properties and the parameters of helical shape are investigated and the result of numerical analysis is presented. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of tensile and deformation behavior of an auxetic plied yarn structure. The basic configuration of the plied structure formed with two soft yarns and two stiff yarns was firstly introduced. Based on this 4-ply helix structure, six kinds of yarn samples were made by different combinations of soft yarns, stiff yarns and twist levels. These yarn samples were first tested and the effects of different design parameters were analyzed. Apart from the tensile test, changes in the internal structure of two samples upon stretching were also studied through microscopic examination. Finally, double helix yarn and 6-ply auxetic yarn were made for a comparative purpose to investigate the effect of helical structure. The study shows that all of the 4-ply auxetic yarn samples exhibit negative Poisson's ratio (NPR) throughout the entire tensile process, and the magnitude of NPR gets larger with a smaller soft yarn diameter, a higher tensile modulus of stiff yarn and a lower twist level. The study also shows that auxetic behavior inside the 4-ply structure is generated by the interplay between the soft yarns and stiff yarns and 4-ply auxetic yarns have the advantages to produce immediate auxetic effect upon stretching. [ABSTRACT FROM AUTHOR]

The present paper concerns two methods: IMD (isotropic material design) and YMD (Young modulus material design) concerning Pareto optimal distributions of the material and its isotropic properties. The merit function is the weighted sum of compliances corresponding to n independent loading conditions. The unit cost of the design is assumed as equal to the trace of the elastic moduli tensor C. In the IMD method, the design variables are the bulk and shear moduli. In the YMD method, the Poisson ratio is assumed as given, possibly non-uniformly distributed in the design domain, the Young modulus being the only design variable. Both the methods reduce to the auxiliary minimization problem involving statically admissible stress fields corresponding to the subsequent loading conditions. The integrand is expressed by a norm of the collection of these stresses, hence has linear growth. The numerical method proposed refers to the primal formulation: it is based on piece-wise polynomial approximation of the set of statically admissible stresses. The exemplary Pareto optimal solutions show that admitting negative values of Poisson's ratio may contribute to a decrease of the total compliances. [ABSTRACT FROM AUTHOR]

The contact problem between two bodies: plate and semi-cylindrical bar is studied in this paper. The analysis concerns the contact pressure distribution along the contact region, as well as the deflection of the plate. Furthermore, the case of a composite plate covered with the auxetic layer is also considered. The influence of the Poisson's ratio of the layer on the behavior of the plate is studied. The contact pressure distribution along the contact area is analyzed using finite element analysis. [ABSTRACT FROM AUTHOR]

This paper reports an experimental investigation on the effect of auxeticity towards impact loads. Both conventional and auxetic polyurethane (PU) foams were subjected to impact drop tests, and the damaged surfaces were visually inspected. Although it is known that auxetic materials resist indentation due to densification along the load line, experimental impact tests on conventional and auxetic PU foams reveal that auxetic foams are not necessarily advantageous over conventional ones for very high impact. This paper proposes a geometrical model that resembles the microstructure of auxetic foams, as well as elucidates both the auxetic behavior and the limiting strength at high impact. [ABSTRACT FROM AUTHOR]

A sandwich-structured composite is a special class of composite materials that is fabricated by attaching two thin but stiff layers to a lightweight but thick core. Composites analyzed in this paper consist of two different materials: auxetic and structural steel. The optimization criterion is minimum compliance for the load case where the frame's top boundary is downward loaded. Outer layers are made of steel while the middle layer is two-phase solid material composite. Only the middle layer is optimized by means of minimization of the objective function defined as the internal strain energy. In the first part of this paper we study the application of the solid isotropic material with penalization (SIMP) model to find the optimal distribution of a given amount of materials in sandwich-structured composite. In the second part we propose a multilayered composite structure in which internal layers surfaces are wavy. In both cases the total energy strain is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce methods of constructing structures with rigid sliding units that exhibit auxetic behavior, namely, have negative Poisson's ratio. First, we illustrate how we can construct 2-dimensional (2D) auxetic structures with bow-tie shaped rigid sliding hexagonal units. Next, we show that we can construct 3-dimensional (3D) auxetic structures by arranging hourglass shaped rigid sliding units in regular triangular configuration or in regular square configuration. Also, we show, through theoretical and numerical analysis, that these structures indeed exhibit auxetic behaviors. [ABSTRACT FROM AUTHOR]

Iron-gallium alloy (galfenol) is a body centered cubic (BCC) magnetostrictive alloy that, like many other BCC metals, is auxetic in the h110i{100} directions. For compositions of 12- 33 at.% gallium, Poisson ratio (n) values as low as 0.7 are observed along these directions in response to a uniaxial elastic force (tensile tests, resonant ultrasound spectroscopy, etc.). In 2014, Raghunath and Flatau first reported that galfenol also exhibits positive strain in both these directions when the uniaxial force applied along the h110i{100} directions is provided solely by a magnetic field, i.e., with no external mechanical/elastic force or stress being applied to the alloy [Raghunath and Flatau, IEEE Trans. Magn. 50(11), 1-4 (2014)]. The observed response is a result of the intrinsic, atomic-scale, bi-directionally coupled magnetoelastic properties of these alloys. In this paper, we advance the understanding of the intrinsic atomic-scale magnetoelastic coupling of the alloy that leads to the observed magnetoelastic auxetic-like behavior by presenting simulations developed based on density functional theory, which we show match the experimental findings and energy-based simulations. The elastic anisotropy and the electronic mechanisms that lead to magnetoelastic auxetic-like behavior in galfenol are discussed. [ABSTRACT FROM AUTHOR]

This paper reports quasi-static and low-kinetic energy impact testing of auxetic and conventional open-cell polyurethane foams. The auxetic foams were fabricated using the established thermo-mechanical process originally developed by Lakes. Converted foams were subject to compression along each dimension to 85% and 70% of the unconverted dimension during the conversion process, corresponding to linear compression ratios of 0.85 and 0.7, respectively. The 0.7 linear compression ratio foams were confirmed to have a re-entrant foam cell structure and to be auxetic. Impact tests were performed for kinetic energies up to 4 J using an instrumented drop rig and high speed video. A flat dropper was employed on isolated foams, and a hemispherical-shaped dropper on foams covered with a rigid polypropylene outer shell layer. The flat dropper tests provide data on the rate dependency of the Poisson's ratio in these foam test specimens. The foam Poisson's ratios were found to be unaffected by the strain rate for the impact energies considered here. Acceleration-time data are reported along with deformation images from the video footage. The auxetic samples displayed a six times reduction in peak acceleration, showing potential in impact protector devices such as shin or thigh protectors in sports equipment applications. [ABSTRACT FROM AUTHOR]

The analysis of auxetic structural elements undergoing transverse shear deformation has so far been largely confined to the first-order shear deformation theory (FSDT), which requires a shear correction factor; analysis using the third-order shear deformation theory (TSDT), which does not require a shear correction factor, is currently lacking in regard to auxetic structural elements. This paper adopts the TSDT to evaluate the elastic stability of isotropic columns with special emphasis on auxetic ones for pinned-pinned columns with springs of equal rotational stiffness at both ends. Results on columns with pinned-pinned (zero stiffness) and fixed-fixed (infinite stiffness) end conditions with square and circular cross sections reveal that auxeticity (i) reduces the transverse shear deformation, (ii) allows the use of classical theories, and (iii) provides higher elastic stability. [ABSTRACT FROM AUTHOR]

Negative Poisson's ratio has already been discovered for many geometrical structures. In most cases, however, the metamaterials built upon such geometries are foams or cellular solids. In this paper, a unidirectional fibrous composite built of two constituent materials of different thermomechanical properties has been studied. The resultant composite is a solid material in its volume. In order to obtain a material of the required properties, both the geometry of fibers and the influence of temperature on both materials have been investigated. [ABSTRACT FROM AUTHOR]

This paper examines a novel approach to designing auxetic textiles. Knit design techniques are used to create auxetic weft-knitted textiles. Development of the appropriate fabrics addresses aesthetic, tactile and subjective design qualities alongside questions of auxetic functionality and testing considerations. The auxetic fabrics produced exhibit expansion in the X- or Y-axis (aligning axes to direction of knitting). The results range from neutral Poisson's ratio to those with a marked expansion in relation to their extension. The fabric discussed uses relief stitch structures and transferred stitches. Variant auxetic knitted fabrics have been produced including related stitch structures and spacer fabrics using the same design processes. The auxetic effects are inspired by common auxetic geometries from the literature. This research aims to combine the methodologies used in knit design and knit engineering to create functional auxetic textiles by using the methods innate to a more traditionally aesthetic design subject. Using quantitative methods to measure the auxetic effect in the samples and qualitative personal reflections on samples, results are kept simple in order to promote dissemination amongst practitioners in different fields. Utilising focus groups with practitioners from various design fields it is also possible to assess the visual, tactile and commercial appeal of the auxetic fabrics whilst they are still in the developmental stage. Using these different methods of feedback into the design stage the theoretical outcome remains simple in terms of language and results stated. The importance of knowledge transfer between disciplines of design and engineering is key to this study. Data capture is imperative encompassing qualitative and quantitative perspectives in conjunction with the use of generically specified terminology. The knowledge transfer afforded by these collaborations is a key output to support the methods chosen for fabric development, those which cross disciplines and appeal to a wide market. Along with an open and experimental approach to conceiving product applications, this will help to place auxetic materials in public view in areas that are novel to the field of auxetic research. [ABSTRACT FROM AUTHOR]

Auxetic fabrics have gained an increasing attention in the auxetic material area in recent years. Especially, auxetic fabrics fabricated based on both weft-knitted and warp-knitted structures have made some important progress. However, all the knitted auxetic fabrics reported so far are fabricated based on 2D knitted structures, although some of the weft-knitted auxetic fabrics are finally formed into 3D forms. This paper reports a novel kind of 3D auxetic fabric fabricated based on a warp-knitted spacer structure with adoption of a special geometrical configuration which is formed with parallelograms. The auxetic behavior of these fabrics is discussed in terms of tensile direction, geometrical parameter, and repeated extension. The shape fitting ability on a spherical surface is also demonstrated. The results shows that the 3D auxetic fabrics have auxetic behavior in all the fabric plane directions and the highest auxetic effect is obtained when stretched in the weft direction of the fabric. The 3D auxetic fabrics also display an excellent shape fitting ability, which makes them very attractive for various applications where fitting to the human body's shape is highly required, such as bra cups, protectors for knees and elbows, shoes covers, etc. [ABSTRACT FROM AUTHOR]

The paper deals with the extended thermodynamical model of thermoelastic interactions in nonlinear elastic solids of anomalous mechanical properties (negative Poisson's ratio materials) including energy dissipation during the thermoelastic damping phenomenon. The model has been based, among others, on Murnaghan's free energy. Numerical simulations show unconventional effects occurring in such materials. [ABSTRACT FROM AUTHOR]

Auxetics are a modern class of material fabricated by altering the material microstructure. Unlike conventional materials, auxetics exhibit a negative Poisson's ratio when subjected to tensile loading. These materials have gained popularity within the research community because of their enhanced properties, such as density, stiffness, fracture toughness and dampening. This paper provides a critical oversight of the auxetic field with particular emphasis to the auxetic foams, due to their low price, easy availability and desirable mechanical properties. Key areas discussed include the fabrication method, the effects played by different parameters (temperature, heating time, cell shape and size and volumetric compression ratio), microstructural models, mechanical properties and potential applications. [ABSTRACT FROM AUTHOR]

Two-parameter analysis of auxetics among the cubic crystals is proposed. A brief analysis of the equivalence of this two-parameter consideration and other approaches is given. The main result of this paper is the classification of partial auxetics with a single dimensionless complex, which is composed of the crystals elastic compliances. The auxetic surface separates the regions with negative and positive Poisson's ratio. The character of its changes with change of the dimensionless complex is determined. The critical value of the complex where a topological rearrangement of the auxetic surface occurs is obtained. The distribution of partial auxetics in zones with different values of the dimensionless complex was found. The sign of another dimensionless parameter influences the location of a region with negative Poisson's ratio relative to the auxetic surface. View of the auxetic boundary for a cubic crystal when the dimensionless elastic parameter is close to the critical value [ABSTRACT FROM AUTHOR]

Auxetics with negative Poisson's ratio (NPR) can expand dimensions along the direction perpendicular to the tensile direction, such as rigid rotation, reentrant and chiral structures, etc. The mechanical performances of chiral metastructures are closely related to internal defects and interactions between defects. In this paper, two types of irregular chiral structures with Gaussian dispersion of circular node positions and missing ligaments are designed, namely: anti‐tetrachiral metastructure and tetrachiral hybrid metastructure. These two types of chiral metastructures are characterized by node radius, ligament thickness, ligament length, the circular node center dispersion range, and missing ligament percentages. Effects of random node distribution range and cell wall missing percentage on the elastic modulus and Poisson's ratio of chiral metastructures are investigated through experimental tests and finite element (FE) simulation systematically. Through dimensionless analysis, it is found that ligament thickness has remarkable influence on the negative Poisson's ratio. Effect of missing ligament on the mechanical properties of the structure is greater than effect of random node center dispersion. With the increase of ligament missing percentage, the resultant modulus of chiral metastructures decreases, and the corresponding NPR increases. [ABSTRACT FROM AUTHOR]

This paper describes the fabrication of polymeric auxetic foam using a quasi tri‐axial compression method. In this method, the conversion process is executed by applying a quasi tri‐axial compression on conventional closed‐cell polyurethane foams. In order to achieve optimum auxetic characteristics, the densification points in various directions are evaluated. In addition, the heating time of the compressed foam is also determined and applied to minimize the residual stress due to the volumetric compression. It leads to the fabrication of auxetic foams with achievable maximum re‐entrancy and minimum collapsed cells without surface creasing. The results also show that the optimized auxetic foam exhibits isotropic behavior compared to its pre‐cursor foam as verified by the morphological analysis. The produced foam has all the desired properties of auxetic foams. The auxetic foam with a negative Poisson's ratio may be have great potential as the supplementary materials in energy absorption and structural applications. [ABSTRACT FROM AUTHOR]

Three 3D models with negative compressibility have been presented in our previous paper [X. Q. Zhou et al., Phys. Status Solidi B 2016, 253, 1977]. However, the 2D mechanism (i.e., wine‐rack mechanism) which we used to design 3D models is so symmetrical that the axial properties of it are equivalent, so we have only focused on geometry features. In this work, an extended study is conducted in order to find a more efficient method to design 3D structures with evident negative compressibility. Through theoretical modeling, the compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for negative compressibility to be exhibited are discussed. The study shows that in addition to the geometry features, negative compressibility effects can also be significantly affected by the arrangement of the framework and layout orientations of 2D mechanism. The compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for the negative compressibility to be exhibited are discussed. It is shown that in addition to the geometry features which have already been widely discussed, the arrangement of the framework and the layout orientations of 2D mechanisms can also have a great influence on the negative compressibility effect. [ABSTRACT FROM AUTHOR]

Stents are scaffold structures that are implanted in body vessels to keep them open. As the image on the front cover illustrates, the use of these biomedical devices can range from supporting blocked arteries in patients suffering from artery stenosis to supporting gullets in patients suffering from oesophageal cancer. The ability of these biomedical devices to fulfil their purpose relies heavily, amongst other things, on how they mechanically behave when they are infl ated and bent to fi t within the vessels. Some of these mechanical aspects are explored in the work by Attard, Gatt and Grima et al. using techniques normally applied to model auxetic structures. The paper on pp. 321–327 shows that with appropriate corrections, the existent models based on simple rotating rigid units can be used to predict the properties of more complex auxetic systems such as the oesophageal stent devices proposed by Ali and Rehman based on the rotating squares model by Grima and Evans. In the paper on pp. 328–337, stents based on hexagonal honeycomb geometries are analysed in terms of their expandability, foreshortening, dogboning and conformability. These effects may have a huge impact on the performance of a stent. The work highlights that, although particular geometries may perform very well in certain aspects, they may perform less well in others. This work has been funded by the Malta Council for Science and Technology through the R&I‐2011‐024 (Smart Stents) project awarded to the University of Malta, HM RD Ltd. part of the Velsud Group, and Tek‐Moulds Precision Engineering Ltd. [ABSTRACT FROM AUTHOR]