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An introduction is presented in which the editor discusses various reports within the issue including the auxetics, conventional foams, and negative Poisson's ratio.

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]

Materials and structures with negative Poisson's ratio are characterized as auxetics. They are interesting for engineering applications due to their non-conventional behavior. However, most of the auxetic structures suffer with a disadvantage that they are difficult to be fabricated because of their complicated geometry structure. To overcome this problem, an auxetic structure made of tubes and corrugated sheets using conventional technology is proposed in this study. Its auxetic effect is investigated by both geometrical analysis and finite element method. For validating the analyses, a real auxetic structure is made with aluminum material and tested under compression condition. All the results obtained show that the proposed structure has very significant negative Poisson's ratio effect under compression. The study has provided a simple way to fabricate auxetic structure for using in a wide range of industrial fields at a low cost. [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]

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]

An introduction is presented in which the editor discusses various reports within the issue on topics including the Poisson's ratio, auxetics and textile fabrics.

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]

A variant of the auxetic helical yarn is explored herein by means of sewing an inextensible thin cord through an elastic fat cord, in a triangular pattern, to form a semi-auxetic yarn. When stretched in the longitudinal direction, the semi-auxetic yarn exhibits conventional and auxetic behavior in the plane perpendicular and parallel, respectively, to the plane which the inextensible thin cord lies on. A simplified model is developed herein to describe the effective Poisson's ratio of the yarn in the conventional and auxetic planes in terms of the initial half angle of the thin cord and the Poisson's ratio of the fat cord. Results show that the Poisson's ratio of the yarn in the auxetic plane decreases and increases with the initial half angle of the thin cord and the Poisson's ratio of the fat cord, respectively, while the Poisson's ratio of the yarn in the conventional plane increases with both parameters. In addition, the dominant parameters for the yarn in the auxetic and conventional planes are the initial half angle of the thin cord and the Poisson's ratio of the fat cord, respectively. Finally, other types of semi-auxetic yarns in the same category are proposed with suggested ways of producing them. [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 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]

Auxetic foams have been widely studied in view of their superior properties and many useful applications and various models have been developed to help explain the auxetic behavior in such foams. One such model involves the description of auxetic foams in terms of rotating units (e.g. the joints where different cell walls meet), a mechanism, which has also been observed experimentally. In the models, the rotating units are taken, to a first approximation, to be representable through rotating rigid triangles, which correspond to the 2D projection of these rotating units and although this model has been improved significantly since it was first proposed, current models still do not fully capture all the deformations that may occur in real foams. In this work, we propose an extended model which not only allows for relative rotation of the units (joints), represented by non-equilateral triangular units, but also for differing amount of material at the joints as well as deformation of the joints themselves, a scenario that is more representative of real auxetic foams. This model shows that, by permitting deformation mechanisms other than rotation of the triangles, the predicted extent of auxeticity decreases when compared to the equivalent idealized rotating rigid triangles model, thus resulting in more plausible predictions of the Poisson's ratios. Furthermore, it is shown that in the manufacturing process, a minimum compression factor, which is dependent on the amount of materials at the joints, is required to obtain an auxetic foam from a conventional foam, as one normally observed in experimental work on foams. [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]

Polyurethane foams processed according to a hybrid mechanical-chemical-thermal (M-Ch-T) process developed at Air Force Institute of Technology (AFIT) have been tested to verify the inner structure deformation after the process. The X-ray microtomography of both the original EUROFOAM S28280 foam and the processed specimens allowed the creation of three-dimensional virtual models of tested specimens and enabled evaluation of homogeneity of foam structures. In order to examine variations in the processed material's inner structure, samples from different locations of the specimen were scanned. Moreover, a foam specimen was divided into nine subspecimens to perform a set of static tests on each of them separately and to check the gradient of properties throughout the sample volume. Presented methods allowed to visualize the inner structure of the processed foams as well as to estimate inhomogeneity. Obtained results will be used for optimization of the manufacturing process. [ABSTRACT FROM AUTHOR]

Auxetics, i.e. systems with a negative Poisson's ratio, exhibit the unexpected property of becoming wider when stretched and narrower when compressed. This property arises from the manner in which the internal geometric units within the system deform when the system is submitted to a stress and may be explained in terms of 'geometry-deformation mechanism' based models. This work considers realistic finite implementations of the well known rotating squares system in the form of (i) a finite planar structure and (ii) a tubular conformation, as one typically finds in stents. It shows that although the existing models of the Poisson's ratios and moduli based on periodic systems may be appropriate to model systems where the geometry/deformation mechanism operate at the micro- or nano- (molecular) level where a system may be considered as a quasi infinite system, corrections to the model may need to be made when one considers finite structures with a small number of repeat units and suggests that for finite systems, especially for the 2D systems, the moduli as predicted by the periodic model may be significantly overestimating the moduli of the real system, even sometimes by as much as 200%. [ABSTRACT FROM AUTHOR]

A re-entrant honeycomb structure made from a novel solid composite based on recycled rubber is an innovative and sustainable solution for engineering applications. This work describes the tensile and failure behaviour of multi re-entrant honeycomb topologies consisting of width, thickness and angle variations. Finite element (FE) models were also developed to simulate tensile tests and failure behaviour of the cellular structures. A Taguchi design (L8) was conducted to determine the effect of each factor on the ultimate strength, ultimate strain, modulus of elasticity, Poisson's ratio and Von Mises stress. The experimental and FE results showed a good correlation, validating the numerical model which was used to perform a parametric analysis on the influence of the cell geometry over the failure behaviour of the structures. The magnitude of Poisson's ratio was significantly affected by the level of each cell geometric parameter. The structures with lower Poisson's ratio values were able to absorb more energy, and consequently, exhibiting less points of failure. It was found the thickness and the width has a significant effect on the tensile properties and failure behaviour. [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]

Elastic properties of the face centered cubic (fcc) phase of particles, interacting through hard-core repulsive Yukawa potential are determined by Monte Carlo (MC) simulations in the NpT ensemble with variable shape of the periodic box. The effects of the Debye screening length ( [ABSTRACT FROM AUTHOR]

The effect of auxeticity on the velocity of elastic wave propagation is investigated herein for isotropic solids. Three types of dimensionless wave velocities are proposed for investigating longitudinal waves in prismatic bars, plane waves of dilatation, plane waves of distortion, and surface waves. Results show that the velocity of surface waves is slightly less than that of plane waves of distortion for conventional solids, but the difference becomes large for auxetic solids. The velocity of longitudinal waves in prismatic bars is higher than that of plane waves of distortion for conventional solids but the gap narrows for solids of the low auxetic range of −0.5 < ν < 0. The velocity of longitudinal waves in prismatic bars become lower than that of plane waves of distortion for intermediate auxetic range of −0.733 < ν < −0.5, and lower than that of surface waves for high auxetic range of −1 < ν < −0.733. [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]

A meshless numerical procedure, known as the method of fundamental solutions, is used to determine elastic deformations of some hypothetical, three-dimensional continua of common or auxetic properties. Demanding boundary conditions, being a mixture of Dirichlet and Neumann ones, are used. The obtained results show very good agreement with those from the standard finite element method. As the applied meshless method is very efficient, it can constitute an interesting alternative to existing methods exploiting various meshes. [ABSTRACT FROM AUTHOR]

The behaviour of the Poisson's ratio is investigated on the basis of derived by the authors explicit equations determining the components of the compliance tensor in an arbitrarily rotated coordinate frame. Clear analytical expressions describing the angular dependencies of the auxetic properties have been found and the crystallographic regions possessing such auxetic behaviour have been revealed for single crystals of elemental metals. This was completed with the straightforward expressions for calculation of the maximum values of auxeticity. The connection between the auxetic properties and the level of anisotropy of single crystals as well as the Cauchy relation has been analysed for various metals with BCC and FCC lattices. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including the dilational materials, the auxetic lattices and the polymorph of silica.

Two-dimensional dilational materials, for which the only easy mode of deformation is dilation are reviewed and connections are drawn between models previously proposed in the literature. Some models, which appear to be dilational materials, but which in fact are not, are also discussed. Finally, four new examples of three-dimensional dilational materials are given. [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]

We describe here a heat-compression protocol used on needle-punched commercial nonwoven fabrics which induces an out-of-plane auxetic response in these treated fabrics. The as-received samples, however, are not auxetic and show a decrease in thickness when stretched uniaxially. Using micro-CT imaging it was found that the vertical fiber bundles/columns, produced in the needle punching step of fabric manufacture, are tilted and buckled as a result of the heat-compression treatment. It is suggested that it is likely the reorientation of these columns during subsequent uniaxial strain that drives thickness increase (auxetic response). Variation of instantaneous Poisson's ratio with axial strain for as-received and treated nonwovens. [ABSTRACT FROM AUTHOR]

Analytical model derivations for predictions of the on-axis Poisson's ratios of the 'α-cristobalite' framework of corner-sharing tetrahedra are presented in full, for the first time, for a previously reported second tetrahedral rotation mechanism. Parametric analyses are performed for each of the three concurrent models (two 2-mode models where dilation acts with each rotation mechanism (the CTM1 and CTM2 models), and the model where all three mechanisms operate (CTM3)) to explore the Poisson's ratio dependency on the key model geometrical and deformation strength parameters. Predictions in good agreement with all experimental on-axis Poisson's ratios specifically for silica α-cristobalite are possible for the new CTM3 model comprising two tetrahedral rotation mechanisms acting concurrently with tetrahedral dilation when direction-dependent strength parameters are employed. This is a significant improvement over the previous analytical model incorporating the tetrahedral dilation and first tetrahedral rotation mechanisms and which only achieved good agreement for loading along the longitudinal x3 axis. [ABSTRACT FROM AUTHOR]

We present the results of an atomistic study on the Poisson's ratios of face-centered cubic metal (001) nanoplates under tensile loading. Here, we find that the behavior of the Poisson's ratios of metal nanoplates is strongly dependent on the characteristics of a phase transformation that takes place in their bulk counterparts as well as on the amount of compressive stress induced in the nanoplates. In addition, we discuss the effects of the nanoplate thickness and temperature on the mechanical behavior of the nanoplates. As the thickness decreases, the amount of compressive stress increases. As a result, the metal nanoplates become more auxetic. Higher temperatures cause the phase transformation to occur sooner. Thus, strongly auxetic nanoplates can be obtained by raising the temperature. In addition to investigating the effects of the thickness and temperature, we compare the behaviors of the Poisson's ratios of (001) nanoplates of six different metals. Interestingly, the behaviors of the Poisson's ratios of the metal nanoplates differ, even though their corresponding bulks have similar and positive Poisson's ratios. This is because the six metals exhibit large differences in their surface stresses as well as in the critical strains for the phase transformation. [ABSTRACT FROM AUTHOR]

Deformation/deflection of thin shells/membranes with clamped boundaries is a common material behaviour relevant to many engineering and medical conditions. A detailed understanding of the deformation mechanisms of different materials/structures with different Poisson's ratios under such a loading condition is of great significance to materials testing and product development. In this work, the deformation of circular elastic membranes with a clamped edge under point loading and finite contact conditions is systematically studied incorporating auxeticity behaviours. The effect of Poisson's ratio on the deformation of the material is investigated and the influence of parameters including sample thickness, indentation depth and indenter size is analysed. The feasibility and limitation of an analytical solution is evaluated. The work shows that the P/ δ3 relationship is applicable to describe the force-displacement data over the membrane domain for both point loading and finite contact conditions. It is shown that negative Poisson's ratios have direct influence on the membrane deformation domain, including the force-displacement curve, the deflection profile and the contact area. Critical factors affecting the P- h curves and the deformation mechanisms are discussed with reference to potential use of the Poisson's ratio effects. [ABSTRACT FROM AUTHOR]

The work describes a cellular structure configuration with a rectangular perforation topology exhibiting auxetic (negative Poisson's ratio) in-plane behaviour. The rectangular voids used in this structure produce a rigid rotating squares effect. Changes in the sizing parameters of aspect ratio, intercell spacing, and number of unit cells are made through non-dimensional modelling. The effects on the key properties of in-plane Poisson's ratio, Young's modulus and shear modulus are investigated. Through numerical modelling and experimental testing the auxetic behaviour is confirmed, with increased negative Poisson's ratio values in comparison to rhomboidal patterns of perforations available in open literature. [ABSTRACT FROM AUTHOR]

Effective properties and dynamic response of a sandwich panel made of two face sheets and auxetic core are analyzed in this study by computer simulations. The inner composite layer is made of a cellular auxetic structure immersed in a filler material of a given Poisson's ratio (filler material fills the voids in structure). Each cell is composed of an auxetic structure (re-entrant honeycomb or rotating square), i.e., exhibiting negative Poisson's ratio without any filler. Influence of filler material on the effective properties of the sandwich panel is investigated. The proposed structure shows interesting structural characteristics and dynamic properties. Our results clearly show that it is possible to create auxetic sandwich panels made of two solid materials with positive Poisson's ratio. This is even possible if the filler material is nearly incompressible, but can move in out-of-plane direction. Moreover, effective Young's modulus of such sandwich panels becomes very large if the Poisson's ratio of the filler material tends to −1. [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]

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]

Analytical and numerical features of the elastic properties of curvilinearly anisotropic six-constant tetragonal nano/microtubes are considered. The analytical formulas for Young's modulus and Poisson's ratio are obtained in the case of axial extension. Numerical calculations are performed using these formulas and data on the elastic constants from the Landolt-Börnstein Handbook. The parametric dependences of Young's modulus and Poisson's ratios for nano/microtubes are analyzed in detail. The basic parameters are elastic compliances, chiral angles, and ratios of the radii of hollow cylindrical tubes. [ABSTRACT FROM AUTHOR]

Special soliton analytical solutions are seeked for the so-called double dispersion equation (or Porubov's equation), which describes the propagation of longitudinal waves in an elastic rod. Using the F-expansion method, a new interesting class of traveling solitary waves is obtained. As a byproduct, the results obtained by other authors for some special cases are regained. Some numerical simulations are also performed. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered. The dependence of the amplitude and the velocity of the solitary waves on Poisson's ratio is discussed in detail. Collisions between some obtained solitary waves are also presented. The simulation results are compared with the obtained exact analytical solutions-the latter reflect the perfect balance between the nonlinearity and dispersion. The comparison indicates that the obtained exact solutions are useful for describing more complicated wave fields studied by numerical simulations. It also indicates that the numerical results for auxetic materials are in better agreement with theoretical solutions than in the case of ordinary materials. Furthermore, one can conclude that the Secant pulse generates solitary waves closer to the analytical predictions than a Gaussian pulse. This is similar to the case of variational method, where the Secant trial function is also more proper than the Gaussian one. [ABSTRACT FROM AUTHOR]

The dynamics of the inner surface of an infinitely long circular-cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long-lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut-off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear-horizontal wave (Love wave) in the short wavelength limit. An axial-radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit. [ABSTRACT FROM AUTHOR]

Propagation of infinitely-lived true surface waves (TSW) and of the evanescent surface resonances (pseudo surface waves, PSW) on the inner surface of a cylindrical cavity in an elastic medium coated with a thin elastic membrane is studied. An analogous flat surface with the same coating is considered as a reference system. The dispersion relations of the true surface waves and of the surface resonances are shown to depend on the interplay between the sound speeds in the substrate and in the covering layer. The short-wavelength limit of the excitations in the cavity is checked to be consistent with the case of the flat surface. Analytical expressions are obtained for the cut-offs and for the asymptotic behaviors of the excitations in the long-wavelength and short wavelength limits. The local surface densities of states (LDOS) as well as the real parts of the Green's functions, i.e., analogues of the reactive power, are calculated. The most eminent anomalies of LDOS, which correspond to the longitudinal resonance, are shown to be located close to the apparently spurious roots of the secular determinant of the surface equations of motion. The roots correspond generally to the total conversion of the longitudinal to transverse bulk waves. These roots show cut-offs, where the life time of the longitudinal resonance increases to infinity. For still lower wave vectors the maxima of LDOS follow the lines of total conversion transverse-to-longitudinal with finite life-times. The radius dependence of the cut-off wave vector in the small-radius limit for a fully symmetric torsional mode is [ABSTRACT FROM AUTHOR]

The Helmholtz wave equation is derived for longitudinal waves in an elastic plate of arbitrary thickness placed in a rigid gantry ensuring a constant width. The whole range of Poisson's ratio allowed for isotropic elastic media constrained in this way is considered. The wave speed is shown to increase under a constant longitudinal compressive stress applied to the front face of the plate and to decrease when the applied stress is tensile. The effect is most pronounced for zero Poisson's ratio and it vanishes for the limiting permitted values, i.e., 1 or −1. The reported results also describe the combined effect of longitudinal stress and Poisson's ratio on the wave speed. These findings provide guidelines for designing devices aimed at a passive control of propagation of longitudinal waves in thin-walled structures. [ABSTRACT FROM AUTHOR]

Using both mathematical and numerical methods, the optimal distributions of material characterized by the Young modulus and Poisson ratio (as well as other moduli of isotropy) maximizing the overall stiffness of an inhomogeneous isotropic elastic 3D body transmitting a given surface loading to a given support are constructed. The overall stiffness of the body is defined as the inverse of the work of external forces on displacements, called here the compliance of the structure. The isoperimetric condition bounds the integral of the trace of the Hooke tensor. It is proved that isotropic composite materials forming the bodies of extremely high stiffness exhibit negative Poisson ratio in large subdomains, which points at the significance of the auxetic material in modern structural design. The obtained results show that the whole range of possible variation of the Poisson ratio is used, from −1 to 1/2, which proves usefulness of the auxetic materials. [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]

In the present work, two new designs of honeycomb structures were presented based on the basic re-entrant structure namely, splined-reentrant and stiffened-reentrant honeycombs. The new structures were designed in order to enhance the in-plane stiffness and maintaining the auxetic behavior of the structure. In this study, finite elements modeling and experimental work were carried out to evaluate the in-plane properties of the new designs. The effect of the geometrical parameters such as rib length and rib thickness of the unit cell of the new designs on the in-plane properties was investigated. Finite elements results showed that the in-plane stiffness of the new designs was improved significantly compared to the basic re-entrant structure. Also, the stiffened-reentrant structure showed better enhancement of the stiffness than the splined-reentrant structure. For example the modulus of elasticity of the stiffened-reentrant structure exceeds 16× that of the basic re-entrant structure in x-direction and was over two times in the y-direction with lower values of the negative Poisson's ratio. Compression tests were carried on honeycomb samples made of steel using laser cutting technique with different geometrical parameters. Test results for the three designs were compared with the finite element results and they were in a good agreement. [ABSTRACT FROM AUTHOR]

A table of contents for the periodical is presented.

Chiral three-dimensional isotropic cubic lattices with rigid cubical nodules and multiple deformable ribs are developed and analyzed via finite element analysis. The lattices exhibit geometrydependent Poisson's ratio that can be tuned to negative values. Poisson's ratio decreases from positive to negative values as the number of cells increases. Isotropy is obtained by adjustment of aspect ratio. The lattices exhibit significant size effects. Such a phenomenon cannot occur in a classical elastic continuum but it can occur in a Cosserat solid. [ABSTRACT FROM AUTHOR]

Recent years have seen a consistent trend in the extension of 2D auxetic models towards 3D ones. This article introduces a 3D auxetic linkage structure by extending the double arrowhead honeycomb structure to an intersecting double arrowhead structure. A geometrical analysis on the basis of rigid linkages with rotational joints shows that auxeticity is manifested in all three orthogonal planes. Results reveal that the geometry, in terms of either the relative linkage lengths or the half angles, can be changed to substantially control the Poisson's ratio. It is herein suggested that functionally graded beams and plates that exhibit gradual change in Poisson's ratio from negative to positive, as well as functionally graded solids with opposing auxeticity trends on different planes, are easily achievable by 3D printing using the intersecting double arrowhead structure, and that further mechanistic analysis be performed. [ABSTRACT FROM AUTHOR]

Elastic properties of the hexagonal crystals under pressure were analyzed. Seven crystals with negative Poisson's ratio (auxetics) were revealed at zero pressure. These are crystals of MoS2, Zn, Be, BeCu (alloy with 2.4 at.% Cu), TiB2, C7H12, and MnAs. Analytical expressions of extreme values of Poisson's ratio and Young's modulus were obtained. For these materials, the variability of Poisson's ratio and Young's modulus was analyzed at pressure change. It was shown that all seven hexagonal auxetics may become completely auxetic under certain pressure values. The variability of the elastic properties of graphite and SiC, being non-auxetics at zero pressure, was considered. These crystals become partially auxetic at negative pressure (-15 GPa for graphite and -56 GPa for silicon carbide) and completely auxetic at -114 and -122 GPa, respectively. The surface of auxeticity v(θ, ψ; p)=0 for hexagonal auxetic MoS2. [ABSTRACT FROM AUTHOR]

We have examined the effect of temperature, pressure, and time on the magnitude of induced auxetic response in postmanufacture- processed needle-punched nonwovens. Different combinations of these processing parameters - temperatures ranging from room temperature to above the glass transition temperature (Tg) of constituent fibers, pressure of 0.49 or 2.45 MPa, and duration of 4 or 24 h - were used to process these nonwovens. This resulted in some permanent compression (defined as "compression set") and in out-of-plane auxetic behavior of the fabric, both of which were found to be proportional to the severity of the processing conditions employed. Milder processing conditions were found to be insufficient in producing significant compression set and hence produced little or no auxetic response. Using micro-CT and optical video microscopy techniques, it was found that the processing conditions caused the fiber bundles present in needle-punched nonwovens to assume a buckled/tilted state, which opened up during mechanical extension and hence were instrumental in the observed thickness increase. Out-of-plane Poisson's ratio with strain for as-received and treated nonwovens. [ABSTRACT FROM AUTHOR]

Auxetic polyproplyene fibres have been produced on a largescale industrial extruder for the first time. A first batch of tests identified a coarse processing window which was then more closely defined by subsequent tests. The effects of barrel temperature, screw speed, take-up speed and quenching (through the parameters of air gap and bath temperature) on the Poisson's ratio and Young's modulus of the fibres were examined. It was found that a temperature of 200 °C, screw speed of 12.5 rpm and take-up speed of either 1.5 or 3.5 rpm produced fibres with a high degree of auxeticity up to 5% strain - significantly increasing the auxetic strain range previously reported for lab-scale extrusions at lower extruder temperatures. Quenching with a water bath reduced the auxeticity, so was not employed as a processing parameter. [ABSTRACT FROM AUTHOR]

This report employed molecular statics simulation and densityfunctional- theory calculation to study the Poisson's ratios of face-centered-cubic materials. We provide numerical and theoretical evidences to show that cubic materials can exhibit auxetic behavior in a principal direction under proper loading conditions. When a stress perpendicular to the loading direction is applied, cubic materials can exhibit a negative Poisson's ratio at finite strain. The negative Poisson's ratio behavior, including its direction and value, is highly dependent on the direction and magnitude of the transversely applied stresses. As a result, we show that it is possible to tune the direction and magnitude of the negative Poisson's ratio behavior of cubic materials by controlling the transverse loadings. [ABSTRACT FROM AUTHOR]

We conducted molecular statics simulations to investigate the negative Poisson's ratio (auxetic behavior) of periodic porous graphene structures based on the rotating rigid unit mechanism. To obtain a negative Poisson's ratio, simple voids were periodically introduced into graphene. We showed that the Poisson's ratio of the designed graphene structure is strongly dependent on the aspect ratio of the voids, and it can approach the theoretical limit of -1.0. More importantly, the graphene periodic structure maintains its auxetic behavior even under large strains (ε~0.20). Hence, it can be employed in a wide range of applications requiring structures that can endure large deformation. In addition, we found that the key factor in the auxeticity of the investigated structures is the deformation occurring at the void tips. [ABSTRACT FROM AUTHOR]

It is demonstrated that the large-amplitude, short-wavelength vibrational modes excited in the lattice can change its elastic properties due to physical and/or geometric nonlinearity of the lattice bonds. Depending on the symmetry of the vibrational mode the symmetry of the elastic properties of the lattice can also change. Using as an example the two-dimensional honeycomb structure with β-FPU pairwise interparticle interactions, we demonstrate that the excitation of a large-amplitude vibrational mode in combination with equiaxial tensile strain can change the sign of the Poisson's ratio from positive to negative, thus leading to the auxetic property of the lattice. It is shown that the considered lattice supports discrete breathers, i.e., spatially localized nonlinear vibrational modes. The excitation of the discrete breathers as a result of the modulational instability of the extended short-wavelength modes is analyzed. Our results contribute to the understanding of the relation between the elastic properties and nonlinear dynamics of the lattices of interacting particles. Extended vibrational modes in the 2D honeycomb lattice presented by the stroboscopic pictures of the particle motion. Excitation of such modes with sufficiently large amplitude in combination with equiaxial tension changes the sign of the Poisson's ratio of the lattice from positive to negative. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations in the isobaric-isothermal ensemble with variable shape of the periodic box are used to study elastic properties of two-dimensional (2D) model systems of hard discs with parallel layers of hard cyclic hexamers. Both the particles in their pure phases form elastically isotropic crystals. However, the crystal of discs shows positive and that of hexamers - negative Poisson's ratio (PR). The studied systems with layers are of low symmetry. Hence, a general analytic formula for the orientational dependence of PR in 2D systems is applied to such systems. It is shown that, by changing parameters of the particles and their relative concentration, as well as orientation of the layers, one can obtain systems which are non-auxetic (their PR is positive), auxetic (their PR is negative), or partially auxetic ones (their PR is negative for some directions and positive for other ones). If the disks and hexamers are interpreted as small molecules, the obtained results indicate that by introducing auxetic nano-layers one can strongly modify PR of crystals or even thin layers. The periodic box with N = 224 particles can be thought of as a model of a thin layer or as a model crystalline structure with parallel horizontal layers built of four hard cyclic hexamer rows in the hard disc system. [ABSTRACT FROM AUTHOR]