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Auxeticity of materials improves several of their mechanical properties, especially shear, impact, and bending resistance. It also improves ability of materials to absorb impact energy as well as the overall stiffness of structures. In this research, authors examine synclastic panels made from novel wood‐based composites. The aim is to determine the force–displacement characteristics during uniaxial compression and obtain the stiffness of the panels. These data allow one to predict the behavior of a panel during two‐axial bending with different support scenarios. Finite element method (FEM) analysis is performed, with the use of model material, to determine the impact of varied facings thickness as well as different types of materials and core structures, on the stiffness of synclastic panels. It is demonstrated that proposed multilayer composites allow forming (technologically difficult) spherical shapes, without additional heat and pressure treatment. The type of an outer layer material strictly determines the usability and ease of two‐axial bending process. Presented composites are interesting materials, that can be adopted into the wood industry as a replacement for traditional materials, e.g., bent plywood. [ABSTRACT FROM AUTHOR]

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]

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]

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]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [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]

Materials with unusual mechanical properties can be potentially used as matrices to create high-performance lightweight composites. The appearance of materials with negative Poisson's ratio (auxetics), has led to the evaluation of auxetic composites for possible engineering applications. Because the experimental evaluation of composites with specific properties is expensive and time consuming, computational modelling and simulation provide efficient alternatives to predict the parameters of the composites. In this paper a finite element method was used to find the engineering constants (Young's modulus and Poisson's ratio) of auxetic composites consisting of concentric cylindrical inclusions made of combinations of auxetic and classic (non-auxetic) materials. It has been observed that not only the mechanical properties of the different composite phases influence the effective mechanical properties of the whole composite, but also the location of the same material phases do matter. [ABSTRACT FROM AUTHOR]

The torsion of a prismatic beam has been a classic problem of structural mechanics since the famous works of Saint-Venant. In this paper, an analysis is extended on a composite beam with elliptical cross-section. We consider a beam in which the elliptical cross-sectionis split into sectors inwhichtwo materials, one of which is auxetic, are distributed alternately. The influence of auxetic phase on the total elastic strain energy is analyzed as well as geometrical parameters representing both the shape of the cross-section, and the arrangements of sectors. An unexpected behavior of a beam with strong auxetic phase is presented as, in the case of selected parameters, the beam with elliptical crosssection is more rigid than the beam with a circular one. [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 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]

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]

Production of piezo‐resistive auxetic sensors is usually carried out through mixing and coating methods. Although these methods are beneficial, Young's modulus of mixed sensors becomes high because of using a high percentage of sensing elements while the durability of coated sensors gets low due to the separation of sensing elements from the sensor surface. This article presents a new core–shell metamaterial model to address the mentioned problems. The shell and the core are produced of polydimethylsiloxane (PDMS) rubber and a mixture of PDMS/graphite powders (73.45 wt% graphite powders), respectively. A finite element model is developed via COMSOL software to predict the electromechanical behaviors of the created sensor and verified by an experimental study. Scanning electron microscope imaging is conducted to detect the separations of the graphite particles. The main important feature of this meta‐sensor is to possess a linear sensitivity due to having zero Poisson's ratio. The advantage of this method is that Young's modulus of the sensor does not decrease (unlike the mixing method), and the sensor‐coated particles do not separate from the sensor after a while (unlike the coating method). The introduced model has advantages that promote potential applications such as using sensory gloves to detect, for instance, human hand movements. [ABSTRACT FROM AUTHOR]

A new method for the production of thin flat and curved auxetic foam sheets by uniaxial compression is reportted in this paper. Detailed optical microscopy and Poisson's ratio measurement by videoextensometry has revealed that the auxetic behaviour is due to a crumpling of the pores through the foam thickness, caused by a uniaxial compression of 40-60% in combination with shear for the curved foams. Poisson's ratio values of up to −3 have been recorded for the curved foams and −0.3 for the flat sheets. [ABSTRACT FROM AUTHOR]

Abstract: Graphene monolayers engineered to adopt a corrugated conformation are found to exhibit very pronounced lateral expansion characteristics upon uniaxial stretching in specific directions, i.e. giant negative Poisson's ratio (auxeticity). Such anomalous properties are manifested in‐plane and may be controlled through the shape and amplitude of the wave‐like pattern of the corrugation, which in the case of graphene may be controlled through the introduction of patterned ‘defects’. This confirms that auxeticity via corrugation can be achieved even at the nanoscale, as demonstrated here for graphene with patterned ‘defects’, suggesting that this mechanism should be operational at different scales of structures, thus providing a new blueprint for the design or manufacture of auxetic materials and metamaterials which can have tailor‐made giant negative Poisson's ratio properties. [ABSTRACT FROM AUTHOR]

Auxetic structures provide an interesting approach to solving engineering problems due to their negative Poisson's ratio, which allows for elongation perpendicular to applied stresses, opposite to a conventional structure's necking behavior. Thus, they can function well in applications requiring compacting the device into a small volume during the deployment (e.g., implants inserted with catheters) or stretchability with area coverage (e.g., stretchable electronics). Fabricating them with shape memory alloys (SMAs) expands the possibilities. The high strains experienced by auxetic structures may become reversible compared to ordinary metals due to superelastic or shape memory effect. This work studies four different auxetic microstructures using thin film SMAs that are capable of surviving strains up to 57.4%. Since these structures are fabricated by layer deposition and lithography, other components, such as microelectronics, can be seamlessly integrated into the fabrication process. These auxetic thin films are investigated for their mechanical behavior under tension for their stretchability and stability. Under tension, thin films are known to show wrinkling instabilities. In two of four designs, the large auxetic behavior leads to wrinkling, while the other two display stable, non‐wrinkling behavior. These designs can be candidates for stretchable electronics, wearable medical devices (e.g., biosensors), or implants (e.g., stents). [ABSTRACT FROM AUTHOR]

This paper reviews 2D auxetic models, including 3D deformation models with 2D auxetic behavior, from mechanism perspective instead of geometrical perspective. On this basis, auxetic models across different geometrical groups can be regrouped into clusters that exhibit analogy in deformation mechanism. Factors that are taken into consideration include the identification of corresponding (i) rotation and non-rotation units, as well as (ii) linkages/joints between rotation and non-rotation units and non-linkages/non-joints across various auxetic models. As a result, five clusters of auxetic models have been identified, in which auxetic models within each cluster are analogous to each other. The identified clusters are those that exhibit: (a) double periodicity in the rotation direction of their rotating units, (b) synchronized rotation direction of their rotation units, (c) single periodicity in the rotation direction of their rotating units, (d) random rotation of their rotation units, and (e) non-rotation of units. Results from this analogy identification place auxetic models in a systematic representation and will enrich future development of auxetic models, particularly those that do not fall within these five clusters. It is proposed that future work includes 3D auxetic models as well as ordering of analogous auxetic models according to their joints or linkage geometries. [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]

An auxetic metamaterial based on a semirotation system is designed herein by combining rigid units of two different shapes, such that each unit cell consists of one nonrotating rhombus and four rotating right triangles. The on‐axes Poisson's ratios are obtained for both infinitesimal and finite deformations by geometrical consideration. The on‐axes Young's moduli of this metamaterial are established by matching the spring potential energy stored at the hinged joints with the strain energy of deformation for the homogenized continuum of the metamaterial. Plotted results describe the interlacing effect of the shape descriptor, the original separation angles, and the change in the separation angle on the on‐axes Poisson's ratio and Young's modulus. The latter is directly proportional to the equivalent spring stiffness per unit cell. In addition to attaining auxetic behavior, this metamaterial can also be designed to achieve specific Young's modulus behavior including extreme stiffness in one of the directions either at infinitesimal or finite deformation. [ABSTRACT FROM AUTHOR]

Cellular solids whose ligaments are made of two distinct materials are constructed for studying their auxeticity and negative thermal expansion via 2D models with the methodology of finite‐element numerical analysis. Three bimaterial cellular models with various radii of ligament curvature (Rc = 5, 8, 11 cm) are analyzed. It is found that when the ligaments comprise aluminum and titanium alloy with Rc = 5 cm, the cellular solid exhibits simultaneous negative effective Poisson's ratio (−0.418) and negative thermal expansion coefficient (−20.82 × 10−6 K−1). When the radius of ligament curvature increases, auxeticity is less pronounced. Positive and negative thermal expansion can be tuned solely by the coefficients of thermal expansion of ligaments' constituents. Furthermore, smaller radii of curvature give rise to larger negative thermal expansion. In addition, modulus mismatch in the bimaterial ligament can be used to tune overall properties. Our findings herein may serve as foundations for the future quantitative design of such cellular materials. In addition, effective Poisson's ratio and coefficient of thermal expansion can be positively or negatively enhanced due to the interplay between the positive and negative phases. Interactions between negative stiffness and larger curvatures may make the system less unstable. [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]

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]

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]

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]

Elastic properties of fcc phases of soft polydisperse spheres, interacting through inverse-power pair potentials [ABSTRACT FROM AUTHOR]

Herein, the effect of symmetric carbon fiber composites laminates with angle‐ply stacking sequences ([±β/±θ]S) in the design of composite piezoelectric energy harvesters (PEHs) is evaluated. Some of those specific stacking sequences also feature negative Poisson's ratio (NPR) or near zero Poisson's ratio (NZPR) through the thickness for ply angles θ < 45°. Six different architectures with similar in‐plane elastic modulus E1 and different positive Poisson's ratio and NPR v13 values are considered here. Finite element models are developed to understand the distribution of the voltage density of the laminates with the different stacking sequences and their bending properties. Experimental tests (three‐point bending and vibration) are also performed. Both the simulations and the experimental results show that the PEH with the stacking sequences of near zero v13 generate the highest power compared with the other composite energy harvesters. The maximum voltage frequency response function (FRF) happens at the fundamental resonance, and the PEH with near zero v13 has also the lowest resonance frequency compared with the other stacking sequences. [ABSTRACT FROM AUTHOR]

A general expression for the Poisson's ratio (PR) of square or 2D cubic materials is discussed in terms of the elastic moduli ratios, X=G/K and Y=G/W, where G and W are the shear moduli, and K is the bulk modulus. The entire XY‐plane is partitioned into nonauxetic, partially auxetic, and auxetic regions by two straight lines. A representation of the XY‐plane with the elastic constant ratio λ=C12/C44 is exploited to investigate 2D square materials under nonzero hydrostatic pressure. It is demonstrated that 2D square materials with λ>0 can be auxetic only under negative pressure. Similarities and differences between the corresponding descriptions of auxetic behavior of cubic 3D materials are pointed out. [ABSTRACT FROM AUTHOR]

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors. [ABSTRACT FROM AUTHOR]

Auxetic materials are a type of novel materials exhibiting negative Poisson's ratio (NPR) with potentials for special applications. Herein, the aim is to optimize the auxetic yarn and fabric manufacturing processes, establish the understanding of the influence of yarn and fabric parameters on the auxeticity of the engineered materials and explore the potential applications of auxetic textile materials. The auxetic yarns are manufactured based on a conversional helical structure composing initially a super elastic polyurethane core and a high modulus Nylon 6,6 binder. A hollow spindle machine is used to produce the auxetic yarn with optimized twisting and delivery speeds. Stable helical yarns with auxetic properties are manufactured using the optimized parameters, and woven fabrics are produced from the selected auxetic yarns in both warp and weft directions. Experiments show that the maximum NPR of helical auxetic yarns reaches a remarkable level of −5.6, and the auxetic fabrics display notable geometric changes compared with the nonauxetic fabrics with the same structural parameters. The auxeticity demonstrated in the fabrics implies applications in areas such as filtration and impact protection. [ABSTRACT FROM AUTHOR]

Honeycombs made from more than one material are proposed and analyzed with the help of finite element simulations. It is shown that such honeycombs are designed to change their shape when subjected to a change in temperature or pressure and can be tailor‐made to exhibit particular thermomechanical properties. It is also shown that the anomalous properties of negative thermal expansion/compressibility can be manifested from honeycombs built from common everyday conventional materials. Applications of such constructs are discussed including their role in the manufacture of smart grips which tighten upon heating. [ABSTRACT FROM AUTHOR]

The flexing of the ligaments at the edge of a finite hexagonal honeycomb array is studied using analytical and numerical methods. It is shown that when compressed axially, the ligaments on the border of a hexagonal honeycomb array bend outwardly in contrast to the interior ligaments that bend to a negligible extent, if at all. This boundary effect reduces the overall auxeticity of re‐entrant hexagonal honeycombs. Analytical expressions that account for the edge effects on the Poisson's ratio and Young's modulus are obtained using Castigliano's second theorem. These are then tested against numerical simulations showing good agreement at least for the values of the parameters used. Additional investigations indicate that the use of a larger ligament thickness for the ligaments residing on the border of the system mitigates this edge effect on the Poisson's ratio. [ABSTRACT FROM AUTHOR]

Auxetic materials behave unconventionally under deformation, which enhances material properties such as resistance to indentation and energy absorption. Auxetics, therefore, have the potential to enhance sporting protective equipment. Herein, finite element modeling, additive manufacturing and impact testing of three auxetic lattices, and a conventional equivalent, with a view to advance auxetic implementation within sports equipment, are explored. The lattices are modeled and impacts are simulated between 1 and 5 J, for flat and hemispherical drop hammers. Simulation outputs including peak impact force, impact duration, maximum axial strain, and Poisson's ratio are compared with experimental results from equivalent impact energies on additively manufactured lattices, using an instrumented drop tower and a high‐speed camera. The simulation and experimental results show broad agreement for all lattices and scenarios, demonstrated by comparative force versus time plots and maximum compression images. The benefits of developing and validating finite element models of three auxetic lattices (and the conventional honeycomb lattice) under various impact scenarios, as a process, are discussed, including material characterization of an exemplar thermoplastic polyurethane. Future work can use the models to further investigate auxetic lattices, selecting and tailoring candidates to further explore their potential application to specific personal protective equipment in sport. [ABSTRACT FROM AUTHOR]

A chiral 3D lattice is designed, made by 3D printing, and studied experimentally. The lattice exhibits squeeze–twist coupling and a Poisson's ratio near zero. Squeeze–twist coupling does not occur in classical elasticity which makes no provision for chirality. By contrast, chiral effects are allowed in Cosserat elasticity. An experimental squeeze–twist coupling strain ratio on the order of unity and a Poisson's ratio near zero are in reasonable agreement with prior finite element analysis of a lattice with similar structure, for which negative Poisson's ratio is anticipated for a sufficient number of cells. [ABSTRACT FROM AUTHOR]

Poisson's ratios of 2D crystals of hard, cyclic tetramers, further referred to as tetramers, are investigated by Monte Carlo (MC) simulations. The tetramers, very simple model molecules, which are composed of four identical hard disks of diameter σ with centers forming a square of side d, are studied in the isobaric–isothermal ensemble. It is found that, at the same thermodynamical parameters, but depending on the anisotropy parameter α=d/σ, the tetramers spontaneously form crystalline phases, representing each of the five Bravais lattices (BLs) which are possible in the 2D space. The following BLs are observed: 1) the oblique (monoclinic) one, 2) the rectangular (orthorhombic) one, 3) the centered rectangular (orthorhombic) one, 4) the hexagonal one, and 5) the square (tetragonal) one. Among them, structures showing auxetic, partially auxetic, and nonauxetic behaviour are found. This fact makes the tetramer an interesting example of a prototype "molecule," which, depending on its shape, assembles materials of all possible behaviors regarding Poisson's ratio. It is worth noting that tetramers with α=1.7 form a strongly auxetic phase that, at the considered thermodynamic conditions, reaches Poisson's ratios varying in the range between −0.589(3) and −0.162(4). [ABSTRACT FROM AUTHOR]

Various clamp designs have been proposed over the years with different degrees of complexity and actual performance vis-à-vis correct grip and reduced impact on the surface strains of the tendon sample. The previous studies all focused on impact on ultimate tensile strain and Young's modulus of the tendons. Here an innovative clamp design is proposed that utilizes the fairly recently available technology that is 3D printing to produce a made-to-measure tendon sleeve that encloses the sample ends and also enables straightforward alignment within the testing equipment. All experiments are carried out using the superficial digital flexor tendons obtained from pig hind legs. The Young's moduli for the linear region of the tendon obtained using this clamp design are very similar to those obtained using the cryo Jaw by other researchers for the same tendon. Furthermore, negative Poisson's ratios are also obtained for the toe-region, in agreement with previous work. [ABSTRACT FROM AUTHOR]

Diamond-like structures, that include sp² and sp³ hybridized carbon atoms, are of considerable interest nowadays. In the present work, various carbon auxetic structures are studied by the combination of molecular dynamics (MD) and analytical approach. Two fullerites based on the fullerene C60 and fullerene-like molecule C48 are investigated as well as diamond-like structures based on other fullerene-like molecules (called fulleranes), carbon nanotubes (called tubulanes) and graphene sheets. MD is used to find the equilibrium states of the structures and calculate compliance and stiffness coefficients for stable configurations. Analytical methods are used to calculate the engineering elastic coefficients (Young's modulus, Poisson's ratio, shear modulus and bulk modulus), and to study their transformation under rotation of the coordinate system. All the considered structures are partial auxetics with the negative value of Poisson's ratio for properly chosen tensile directions. It is shown that some of these structures, in a particular tension direction, have a very high Young's modulus, that is, 1852GPa for tubulane TA6. [ABSTRACT FROM AUTHOR]

Perforated systems constitute one of the most important classes of mechanical metamaterials. In this work, two types of "I"-shaped slit perforation patterns are proposed which may be used to design perforated systems that mimic the deformation mechanisms of a variety of re-entrant and anti-tetrachiral honeycomb systems. Using finite element analysis, it is shown how these systems have the potential to exhibit a large spectrum of negative Poisson's ratios, ranging from extremely negative to zero, which are retained over a wide tensile strain range. A detailed analysis of the deformation behavior of these systems is also presented along with a comparison of the changes in overall expansion and Poisson's ratios of both systems observed upon loading with those predicted by previously formulated theoretical models of re-entrant and anti-tetrachiral systems. It is hoped that this work will be of considerable aid in the efforts of scientists to understand the underlying principles governing the production of auxetic mechanical metamaterials through the use of perforations and also stimulate further research on how these and similar mechanisms may be implemented in perforated systems to design other metamaterials with anomalous mechanical properties. [ABSTRACT FROM AUTHOR]

An extensive investigation is carried out on the missing rib square grid structure using finite element simulations. This showed that, in the cases considered in this study, the type of deformation is primarily dependent on the ratio of the thickness of different ribs with the structure behaving like an anti-tetrachiral at particular ratios. The analysis also showed that the ability of the structure to deform predominantly through the bending of the ligament allows it to achieve much more negative values of the Poisson's ratio than previously reported. Confirmation of the numerical results is obtained through experimental methods involving the 3D printing of representative structures which are subsequently subjected to compression. [ABSTRACT FROM AUTHOR]

Poly(phenylacetylene) sheets that mimic the geometry of a wine-rack-like structure have been predicted to exhibit negative Poisson's ratios off-axis. However, their potential to exhibit negative linear compressibility (NLC) has remained largely unexplored. In this work, the compressibility and other mechanical properties of wine-rack-like poly(phenylacetylene) networks with 1,2,4,5 tetra-substituted phenyls as well as their equivalent with allene or cyclobutadiene centres are simulated to assess their ability to exhibit negative linear compressibility on-axis and off-axis. It is shown that some of these systems can indeed exhibit negative linear compressibility whilst others exhibit a near-zero compressibility. The results are compared to the compressibility properties of other poly(phenylacetylene) networks reported in literature as well as with those predicted from the analytical model for an idealised wine-rack structure deforming through hinging. Results suggest that these mechanical properties are arising from a wine-rack-like mechanism, and there is a good agreement with the theoretical model, especially for systems with longer acetylene chains whose geometry is closer to that of the idealised wine-rack. [ABSTRACT FROM AUTHOR]

Auxetic materials have a negative Poisson's ratio, which can enhance other properties. Greater indentation resistance and energy absorption, as well as synclastic curvature, could lend auxetic materials well to protective sports equipment and clothing. Sheets of foam often form padding within protective equipment, but producing large homogenous auxetic foam samples is challenging. The aim of this work was to investigate techniques to fabricate large thin sheets of auxetic foam, to facilitate future production and testing of prototype sports equipment utilizing this material. A mold was developed to fabricate sheets of auxetic foam − with planar dimensions measuring 350 × 350 mm − using the thermo-mechanical process. The mold utilized through-thickness rods to control lateral compression of foam. Sheets of auxetic foam measuring 10 × 350 × 350 mmd were fabricated and characterized. Each sheet was cut into nine segments, with density measurements used to determine how evenly the foam had been compressed during fabrication. Specimens cut from corner and centre segments were subject to quasi-static extension up to 30% to obtain stress versus strain relationships, with Digital Image Correlation used to determine Poisson's ratio. Specimens cut from the corner tended to have a marginally higher density, lower stiffness and more consistent negative Poisson's ratio compared to those from the centre, indicating some inconsistency in the conversion process. Future work could look to improve fabrication techniques for large thin homogenous sheets of auxetic foam. [ABSTRACT FROM AUTHOR]

We investigate auxetic isotropic elastic materials with the Poisson's ratio of exactly −1 and isotropic materials with the Poisson's ratio of near 0.5 (incompressible). In both cases the energy is not positive definite, which can lead to the material instability. In incompressible materials, the instability manifests itself in the emergence of non-uniform displacement distribution. Investigation of the behavior of such materials with respect to damage or crack accumulation is based on the notion that during the instantaneous process of fracture formation, the fracture acts as a negative stiffness element; after the fracture is formed, it immediately turns into a conventional fracture with usual positive stiffness. We demonstrate that the cracks formed due to tensile or combined tensile and shear fracturing of the material are capable of momentarily bringing the Poisson's ratio of nearly incompressible material to 0.5, which instantaneously turns the material into unstable. On the other hand, the formation of shear cracks leads to reduction in the Poisson's ratio bringing the material away from the point of instability. Opposite to this, cracks of all kinds do not change the Poisson's ratio in extreme auxetics (the Poisson's ratio equal to −1). Thus the auxetic materials remain stable with respect to fracture formation. [ABSTRACT FROM AUTHOR]

An exploration by analytical method has been made herein for a mechanism-based structure that involves a two-dimensional array of rings and a three-dimensional array of double-rings, with short fixed rods and long sliding rods attached at the outer and inner surfaces of the rings, respectively. Based on the theory of thin rings, effective Poisson's ratio and effective coefficient of thermal expansion (CTE) models have been obtained for single-ring structures, pole-loaded double-ring structures, and equator-loaded double-ring structures. Results establish a very strong correlation between these effective properties with the ring radius and rod lengths. In addition, the analysis of four of the double-ring structures reveals that the sign of Poisson's ratio is dependent on the direction of loading. An example application is demonstrated herein in which positive thermal expansion rings, used in conjunction with rigid rods, enable the design of an overall zero thermal expansion structure (i.e., minimal thermal stress) with tunable negative thermal expansion internal microstructure for use as sieve. Finally, it is herein shown that, by judicious positioning of the short fixed rods and/or long sliding rods, one may possibly obtain various combinations of positive and negative CTEs with positive and negative Poisson's ratio. [ABSTRACT FROM AUTHOR]

Size effects are explored experimentally in a tetragonal lattice structure. Size dependence of rigidity is nonclassical elastic and is interpreted via Cosserat elasticity. The characteristic lengths are about a third the cell size. The Cosserat characteristic length for torsion is [ABSTRACT FROM AUTHOR]

Effective Young's modulus and Poisson's ratios of two-layered cylindrical hollow tubes made of cubic crystals (auxetics and nonauxetics) are considered. An analysis of longitudinal tension of stretching tubes is performed within the framework of curvilinear-anisotropic elasticity and Saint-Venant's approximation. Analytical dependences of effective Young's modulus on the compliance coefficients of the initial crystals and layer thickness as ratio of composites auxetics-nonauxetics are obtained. Deviations from the 'rule of mixtures' predictions which increase with increasing Young's modulus of initial nonauxetics are demonstrated. It is found that effective Poisson's ratios of two-layered tubes depend on the ratio of their thicknesses, the dimensionless combinations of compliance coefficients and a dimensionless radial distance. An effect of tube components on negativeness of effective Poisson's ratio of the composite auxetics-nonauxetics proved to be strongly dependent on the value of Young's modulus for nonauxetic component. It is shown that effective Poisson's ratios for some characteristics of the initial crystals and ratios of layer thicknesses may fall outside the limits on Poisson's ratios of isotropic materials. It is shown that many two-layered tubes composed of pairs of nonauxetics can have large negative effective Poisson's ratios. [ABSTRACT FROM AUTHOR]

A novel class of hexagonal nanoscale honeycombs made from penta and tetra substituted polyphenlyacetylenes is proposed and modeled as crystalline systems using force-field based simulations. It is shown that, in-plane, these systems behave rather similarly to crystalline forms of graphyne, graphdiyne, and other fully substituted equivalents but benefit from the presence of larger pores which makes them less stiff and may enable them to be used in a wider range of applications such as nanofiltration. It is also shown that at large strains these systems have the potential to exhibit auxetic out-of-plane behaviour, a property which can be manifested in other triangulated systems and can be explained from buckling of some nanoribs in the systems. [ABSTRACT FROM AUTHOR]

We simulate, analyse and compare the mechanical properties of a number of molecular sheet-like systems based on fully substituted, penta-substituted, tetra-substituted and tri-substituted poly(phenylacetylene) using static force-field based methods. The networks are modeled in a 3D environment with and without inter-layer interactions in analogy to graphite and graphene respectively. It is shown that by varying the type of substitution and the length of the acetylene chain, one may control the mechanical properties of such systems. In particular, it is shown that poly(phenylacetylene) systems can be specifically designed to exhibit negative Poisson's ratio, and that the stiffness can be controlled in an independent manner from the Poisson's ratios. This is significant as it highlights the fact that such systems can be tailored to exhibit a particular set of mechanical properties. [ABSTRACT FROM AUTHOR]

Although high heels are known to affect the biomechanics of human movement, most notably by increasing forefoot plantar pressure, it is commonly worn due to the influence of fashion. To deal with the resulting clinical issues, some prescriptions include the use of cushioning pads to redistribute the plantar loads and increase comfort. This preliminary study has sought to investigate whether auxetic foam would be a good candidate for the redistribution of plantar loafing in the forefoot when compared to a more traditional material. From the results obtained, it was shown that auxetic foam demonstrated a decrease in forefoot peak plantar pressure while a commercial product, a material traditionally used for plantar cover paddings, increased pressure in the region of the second-fourth Metatarsophalangeal Joint. This demonstrates the potential for auxetic materials to become the material of choice for such applications, especially since it can be further remodeled until its properties can produce a significant forefoot pressure reduction. [ABSTRACT FROM AUTHOR]

The microstructure of the manmade auxetic materials always involve inherited porosity and sharp corners, where the stress concentration occurred. We have proposed a novel kind of non-porous smooth curve sheet which exhibits a negative Poisson's ratio and has a low stress concentration factor. The auxetic response was validated by good qualitative and quantitative agreements between the tensile experiments and numerical analysis of array model. Using the experimentally validated finite element model, the parametric study on the evolution of the macroscopic Poisson's ratio, the stress concentration factor on the geometry parameters and the parental material properties were investigated. This one phase auxetic smooth curve sheet, which is simple to manufacture and assemble into 3D structures, may be used in a variety of industrial applications. [ABSTRACT FROM AUTHOR]

This article describes the rules and procedures for designing a three-dimensional (3D) antitetrachiral structure that achieves a negative Poisson's ratio. Numerical analysis and experimental validation showed good agreement between the deformations and Poisson's ratios. Moreover, the proposed auxetic structure displayed anisotropic behavior in x- and y-directional compression as well as isotropic behavior in z-directional compression. The parametric study and design examples presented in this article demonstrate the relationships among the Poisson's ratio, effective Young's modulus, porosity, and geometry of the proposed structure, and provide insights into the potential applications for future auxetic designs. [ABSTRACT FROM AUTHOR]

Optimization of structures with complex shapes is a big challenge for computational physics. Results of numerical calculations show that composite or sandwich panel structures have a great influence on their effective properties. This article presents numerical results of optimization of sandwich panel properties. Calculations were provided for a three-layer sandwich two-phase composite. Optimization techniques were used for minimization of the effective Poisson's ratio of the core. The resultant composite structure exhibits a negative Poisson's ratio (NPR), although all its constituents are characterized by positive values of the Poisson's ratio. The structure of the composite is completely filled with solid materials, hence no voids appear within its whole volume. To find a solution, the finite-element method combined with an optimization algorithm MMA (method of moving asymptotes) was used. For the purpose of analysis, the material parameters were written by means of the shape interpolation SIMP (solid isotropic material with penalization) scheme. [ABSTRACT FROM AUTHOR]

The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau-type phase field model in two dimensions. The model may exhibit a single-well (doublewell) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature-induced solid-solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single-domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress-strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems. [ABSTRACT FROM AUTHOR]