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Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson’s ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Prototyping of three-dimensional mechanical metamaterials that exhibit negative Poisson’s ratio is usually performed through additive manufacturing. Although this technique has a huge potential, its use to engineer mechanical metamaterials for consumer products is still challenging. In this work, a novel design method is being proposed where 3D auxetic metamaterials can be produced by introducing continuous voids of constant cross-sectional area. Such voids would be inserted at strategic positions in different perpendicular planes of a solid block to obtain a continuous three-dimensional mechanical metamaterial that can exhibit the desired mechanical characteristics. The use of continuous voids to design the 3D meatamaterial makes it possible to use additive manufacturing, subtractive manufacturing as well as casting to produce these systems. The proposed design method is explained by using continuous voids having a diamond shaped cross-sectional area. The resulting group of structures can be described as connected polygons and were found to exhibit a negative or zero Poisson’s ratio. The analysed systems were also found to have a strain independent Poisson’s ratio up to at least 7% strain. The proposed design method can thus facilitate the availability of three dimensional auxetic metamaterials in the consumer market which to date is conspicuous by their absence.

The mechanical properties of single crystals boron arsenate, BAsO4, are simulated through density functional theory simulations over a wide range of pressures from −10 to +90 GPa. It was shown that the elastic constants, as well as the extent of auxeticity, are highly pressure dependent. In particular, the Poisson’s ratio in the (001) plane for stretching in the [100] crystallographic direction is only found to be negative up to pressures of ∼30 GPa, with maximum auxeticity being predicted to occur at ∼15 GPa. It was also shown that the extent of auxetic behavior may be explained through two mechanisms that act concurrently, namely (i) a mechanism which involves rotations of tetrahedra that project in the (001) plane in the form of “rotating semi-rigid squares” and (ii) a mechanism, which is being reported for the first time, whereby the tetrahedra deform and become flatter.

Olympic-style sliding-seat rowing is a sport that has been extensively researched, with studies investigating aspects related to the physiology, biomechanics, kinematics, and the performance of rowers. In contrast, studies on the more classic form of fixed-seat rowing are sparse. The aim of this study is to address this lacuna by analysing for the first time the specific kinematics of fixed-seat rowing as practised by able-bodied athletes, thus (i) documenting how this technique is performed in a manner that is replicable by others and (ii) showing how this technique compares and contrasts with the more standard sliding-seat technique. Fixed-seat rowing was replicated in a biomechanics laboratory where experienced fixed-seat rowers, marked with reflective markers following the modified Helen–Hayes model, were asked to row in a manner that mimics rowing on a fixed-seat boat. The findings from this study, complimented with data gathered through the observation of athletes rowing on water, were compared to sliding-seat ergometer rowing and other control experiments. The results show that, in fixed-seat rowing, there is more forward and backward thoracic movement than in sliding-seat rowing (75–77° vs. 44–52°, p < 0.0005). Tilting of the upper body stems was noted to result from rotations around the pelvis, as in sliding-seat rowing, rather than from spinal movements. The results also confirmed knee flexion in fixed-seat rowing with a range of motion of 30–35°. This is less pronounced than in standard-seat rowing, but not insignificant. These findings provide a biomechanical explanation as to why fixed-seat rowers do not have an increased risk of back injuries when compared with their sliding-seat counterparts. They also provide athletes, coaches, and related personnel with precise and detailed information of how fixed-seat rowing is performed so that they may formulate better and more specific evidence-based training programs to meliorate technique and performance.

Purpose: The purpose of this study was to look for a new, simple, and fast method of assessing and monitoring indoor race performance and to assess the relationship between 20 s, 60 s, and 2000 m indoor rowing performances of youth rowers to evaluate their anaerobic profile.Methods: For three consecutive days, 17 young able-bodied male rowers (15.8 ± 2.0 years), performed three tests (20 s, 60 s, and 2000 m) on a rowing ergometer. Mean power (W20, W60, and W2000) and 2000 m time (t2000) were considered for the analysis. In addition, 14 athletes (15–18 years) performed a 20 s, 60 s, and 2000 m tests and used this as a control group. To define the anaerobic profile of the athletes, W20 and W60 were normalized as percentages of W2000. Associations between variables were determined by means of the Pearson correlation coefficient (r).Results: Mean power decreased with increasing test duration (W20 = 525.1 ± 113.7 W; W60 = 476.1 ± 91.0 W; W2000=312.9 ± 56.0 W) and negative correlations emerged between t2000 (418.5 ± 23.1 s) and W20 (r = −0.952, p < 0.0001) and W60 (r = −0.930, p < 0.0001).Conclusion: These findings indicate that W20 and W60 are significant predictors of 2000 m rowing ergometer performances. Furthermore, normalized W20 and W60 can be used to evaluate athletes and as a reference for planning anaerobic training sessions, on a rowing ergometer.

This work presents a qualitative and quantitative pilot study which explores the kinematics of Venetian style forward-facing standing rowing as practised by able-bodied competitive athletes. The technique, made famous by the gondoliers, was replicated in a biomechanics laboratory by a cohort of four experienced rowers who compete in this style at National Level events in Malta. Athletes were marked with reflective markers following the modified Helen Hayes model and asked to row in a manner which mimics their on-water practise and recorded using a Vicon optoelectronic motion capture system. Data collected were compared to its equivalent using a standard sliding-seat ergometer as well as data collated from observations of athletes rowing on water, thus permitting the documentation of the manner of how this technique is performed. It was shown that this rowing style is characterised by rather asymmetric and complex kinematics, particularly upper-body movements which provides the athlete with a total-body workout involving all major muscle groups working either isometrically, to provide stability, or actively.

Negative thermal expansion (NTE) materials and structures exhibit the anomalous property of shrinking rather than expanding when heated. This work examines the potential of multi-material planar re-entrant and non-re-entrant honeycombs to exhibit anomalous thermal expansion properties. Expressions for the coefficient of thermal expansion as a function of the geometric parameters and intrinsic thermal expansion properties were derived for any in-plane direction. It was shown that re-entrant honeycombs, a metamaterial which is well known for its auxetic characteristics, can be made to exhibit NTE in specific directions when constructed from conventional positive thermal expansion (PTE) materials, provided that the slanting ligaments expand more than the vertical ligaments when heated and that the geometry is amenable. Conversely, it was shown that the construction of such honeycombs from NTE components will not necessarily result in a system which exhibits NTE in all directions. Furthermore, conditions which result in honeycombs demonstrating zero thermal expansion (ZTE) coefficients in specific directions were also explored.

Boron arsenate, BAsO4, is a β-cristobalite-like crystal which has been reported to exhibit the rather unusual property of negative linear compressibility behaviour at elevated pressures, that is expanding rather than shrinking in a linear dimension when subjected to pressure. This work proposes a ‘geometry—deformation mechanism’-based mathematical model to aid the discernment of the manner how this anomalous pressure behaviour is achieved. The model makes use of data obtained from DFT simulations over an extended range of pressures, including extreme pressure conditions, and rigorously explains the macroscopic properties of this material in terms of the nanoscale deformations. More specifically, through this model, it was possible to decipher the different contributions to the deformation mechanism and compressibility properties of BAsO4. Moreover, for the first time, it was shown that a rule related to the sum of angles of tetrahedrally coordinated atoms is so robust that it applies at the extreme pressures studied here.

In this work, through the use of a theoretical model and experimental testing, we investigate a novel three-dimensional mechanical metamaterial composed of structural units consisting of two arrowhead-like elements with magnetic inclusions. We show that such system has a capability to exhibit negative Poisson's ratio and negative incremental stiffness at the same time. We also show that both the type of the stiffness exhibited by the system and its magnitude can be solely controlled via the orientation of magnetic inclusions within the structure and the magnitude of the magnetic moment associated with magnetic inclusions respectively. More specifically, for a particular example of magnetic inclusions used in the experiment, the stiffness could assume an arbitrary value from the range approximately between −5 kN/m and 5 kN/m depending on the stage of the mechanical deformation and aforementioned factors. This range can be also conveniently adjusted depending on the size and properties of magnetic inclusions. This in turn allows to adjust mechanical response of the considered structure in accordance to a particular application without a need of reconstructing the system which would not normally be possible for conventional nonmagnetic systems attributing negative stiffness to their elastic properties. Keywords: Mechanical metamaterials, Composites, Auxetic behaviour, Magnetic inclusions, Negative stiffness

Negative Poisson’s ratio materials (called auxetics) reshape our centuries-long understanding of the elastic properties of materials. Their vast set of potential applications drives us to search for auxetic properties in real systems and to create new materials with those properties. One of the ways to achieve the latter is to modify the elastic properties of existing materials. Studying the impact of inclusions in a crystalline lattice on macroscopic elastic properties is one of such possibilities. This article presents computer studies of elastic properties of f.c.c. hard sphere crystals with structural modifications. The studies were performed with numerical methods, using Monte Carlo simulations. Inclusions take the form of periodic arrays of nanochannels filled by hard spheres of another diameter. The resulting system is made up of two types of particles that differ in size. Two different layouts of mutually orthogonal nanochannels are considered. It is shown that with careful choice of inclusions, not only can one impact elastic properties by eliminating auxetic properties while maintaining the effective cubic symmetry, but also one can control the anisotropy of the cubic system.

Background and Objectives: Rowing is a sport that involves constant gripping, pulling/pushing, and rotational movements of the hands, in a cyclic periodic manner with every stroke, with hundreds of strokes being taken within a short period of time. Dermatological issues on rowers’ hands (fingers and palms) in the form of blisters and calluses are common knowledge within the community, but their prevalence and the rower’s perceptions and pain tolerance to them has never been systematically evaluated. This work addresses these lacunae. Materials and Methods: Analysis of data collected from a survey on a sample of competitive (117) and noncompetitive rowers (28) who row on-water (total 145). Results: It was found that approximately 69% of rowers participating in this study have calluses on their hands for most of their time (considered by them as not painful). The incidence of blisters was found to be lower (but perceived as more painful). Their incidence was found to be fairly independent of the frequency and intensity of training, but they seem to affect most rowers equally at the beginning of season or during a change of position (nonconditioned hands). Blisters and calluses were reported to be mainly located on the proximal phalanges and metacarpo-phalangeal joint area of both hands, i.e., on the lower parts of the fingers and the upper inner palms. Conclusions: Rowers demonstrated a sense of acceptance of these dermatological issues, even a sense of pride in what they represent. The incidence of blisters becoming infected was estimated to be so low that most rowers would not have encountered such serious, albeit rare, consequences.

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very significant changes in its elastic properties. The use of inclusions in the form of joined (mutually orthogonal) layers and channels showed that the resulting tetragonal system exhibited a complete lack of auxetic properties when the inclusion spheres reached sufficiently large diameter. Moreover, it was very surprising that this hybrid inclusion, which can completely eliminate auxeticity, was composed of components that, alone, in these conditions, enhanced the auxeticity either slightly (layer) or strongly (channel). The study was performed with computer simulations using the Monte Carlo method in the isothermal-isobaric (NpT) ensemble with a variable box shape.

The structural and mechanical properties of various types of poly(phenylacetylene) crystalline networked polymers which stack in the third direction in a graphite-like manner have been the subject of extensive research over the past few years. These studies have suggested that depending on the particular manner of substitution of the phenyls, it is possible to achieve some very interesting mechanical properties, which include, in some cases, negative Poisson’s ratio (NPR) and/or negative linear compressibility (NLC). The current study investigated how alternatives to these systems can be designed, and specifically tailor-made to exhibit desirable anomalous properties, such as NPR and NLC, through the replacement of the acetylene chains with ethylene chains, so as to produce the poly(phenylethylene) equivalents. Using force field-based simulations, via the use of the polymer consistent force-field (PCFF) it was noted that, to a first approximation, these systems mirror some of the analogous properties exhibited by their poly(phenylacetylene) counterparts. In particular, poly(phenylethylene) systems built from 1234- and 1245-substituted phenyls exhibited negative Poisson’s ratios, with the latter also exhibiting negative linear compressibility. This anomalous behaviour, mirrors, to some extent, that exhibited by their poly(phenylacetylene) counterparts, albeit some differences were noted, such as a reduction in the degrees of auxeticity. It was also noted that the poly(phenylethylene) systems modelled here tend to stack in the third direction, in a different manner than their poly(phenylacetylene) analogues, which difference is likely to be the factor for such reduction in auxeticity.

Boron arsenate, BAsO4, is crystalline material (I4¯ group) that was recently shown to be auxetic in its (001) plane for loading in any direction in this plane, and, which exhibits negative linear compressibility at elevated pressured in its [001] direction. This work presents and discusses the results of extensive density functional theory (DFT) based simulations aimed at studying deformations that such crystals undergo when subjected to shear loading in an attempt to obtain a better insight into the manner in which this material responds to mechanical loads. The deformations for shearing in the (001) plane are described in terms of the ‘rotating squares’ model, which was used to explain the auxeticity in the same plane where it was shown that shear loading results primarily in deformations which make the ‘squares’ become ‘parallelogram-like’ rather than rotate. This lack of rigidity in projected ‘squares’ was discussed by looking at changes in bond lengths and bond angles.

In this work, we use computer simulations (Molecular Dynamics) to analyse the behaviour of a specific auxetic hierarchical mechanical metamaterial composed of square-like elements. We show that, depending on the design of hinges connecting structural elements, the system can exhibit a controllable behaviour where different hierarchical levels can deform to the desired extent. We also show that the use of different hinges within the same structure can enhance the control over its deformation and mechanical properties, whose results can be applied to other mechanical metamaterials. In addition, we analyse the effect of the size of the system as well as the variation in the stiffness of its hinges on the range of the exhibited auxetic behaviour (negative Poisson’s ratio). Finally, it is discussed that the concept presented in this work can be used amongst others in the design of highly efficient protective devices capable of adjusting their response to a specific application.

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.

Auxetics (negative Poisson’s ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism—termed the ‘triangular elongation mechanism’—leading to such anomalous behavior is presented and discussed through an analytical model. Amongst other things, it is shown that this novel mechanism, when combined with the well-known ‘rotating squares’ model, can generate giant negative Poisson’s ratios when the system is stretched.

Abstract This letter re-assesses a publication in the Journal of Cardiothoracic Surgery entitled ‘Vibration transmittance measures sternotomy stability – a preliminary study in human cadavers.’ The roles of ultrasound in testing for sternotomy stability and that of stress vibration transmittance in cases of fracture of the posterior table of the sternum or in hairline undisplaced fractures are examined in view of their differing sound wave frequency ranges.

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them.

Foams are commonly used for cushioning in protective sporting equipment. Volumetrically compressing open-cell polyurethane foam buckles cell ribs creating a re-entrant structure—set by heating then cooling—which can impart auxetic behaviour. Theoretically, auxetic materials improve impact protection by increasing indentation resistance and energy absorption, potentially reducing sporting injuries and burdens on individuals, health services and national economies. In previous work, auxetic foam exhibited ~3 to ~8 times lower peak force (compared to its conventional counterpart) under impacts adopted from tests used to certify protective sporting equipment. Increases to the foam’s density and changes to stress/strain relationships (from fabrication) mean Poisson’s ratio’s contribution to reduced peak forces under impact is unclear. This work presents a simple fabrication method for foam samples with comparable density and linear stress/strain relationship, but different Poisson’s ratios ranging between 0.1 and −0.3, an important step in assessing the Poisson’s ratio’s contribution to impact force attenuation.

Auxetic materials exhibit the very unusual property of becoming wider when stretched and narrower when compressed, – they have a negative Poisson’s ratio. This unusual behaviour is the source of many desired effects in the materials’ properties and it is therefore, no wonder that auxetics are described as being superior to conventional materials in many practical applications. Here we make use of force-field based molecular modelling simulations in order to investigate the mechanical properties of polypehyleacetylene systems known as (n, m)-flexyne and (n, m)-reflexyne in an attempt to extend the existing knowledge there is regarding these systems. These systems have already attracted considerable consideration since negative on-axis Poisson’s ratios have been discovered for the reflexynes. We first developed a methodology for the modelling and property determination of flexyne and reflexyne network systems which we validated against existing published data. Then, extended the study to prove the simulated results were independent of the modelling methodology or the force-field used. In particular, we showed that on-axis auxeticity in the reflexynes is a force-field independent property, i.e. a property which is not an artefact of the simulations but a property which is likely to be present in the real materials if these were to be synthesised. We also studied and reported the shear behaviour of these systems were we show that the flexynes and reflexynes have very low shear moduli, a property which regrettably limits the prospects of these systems in many practical applications. Finally we examine the in-plane off-axis mechanical properties of the systems and we report that in general, these mechanical properties are highly dependent on the direction of loading. We also find that the auxeticity exhibited by the reflexynes on-axis is lost when these systems are loaded off axis since the Poisson’s ratios becomes positive very rapidly as the structure is stretched slightly off-axis (e.g. 15deg off-axis). This is once again of great practical significance as it highlights another major limitation of these systems in their use as auxetics.

This paper investigates the suitability of the General Utility Lattice Program (GULP) for studying auxetic materials at the molecular level. GULP is a force-field based molecular modelling package which incorporates the ‘core-shell’ model for simulating polarisability. A validation procedure was performed where the capability of GULP to reproduce the structural and mechanical properties of SOD (a zeolite for which the single crystalline elastic constants have been experimentally measured). It was found that not all GULP libraries (force-fields) could reproduce these properties, although the ‘Catlow 1992’ and ‘Sauer 1997’ libraries were found the produce good results. These libraries were then used to study the all-silica forms of various ‘presumably auxetic’ zeolites. The simulations generally confirmed the conclusions reported in earlier studies, and in particular, the fibrous zeolites THO, NAT and EDI where once again shown to be auxetic in the (001) plane. A study was also performed aimed at assessing the effect of interstitial species on the mechanical properties of NAT where it was shown that these species reduce the auxetic effect. This is very significant as once again we have confirmed the potential of these materials as molecular level auxetics, and hopefully, these results will result in generating more interest into the fascinating materials which could be used in many practical applications (e.g. tuneable molecular sieves).

This study considers a 3D basic unit-cell proposed for auxetic and non-auxetic foams namely the elongated hexagonal dodecahedron deforming through changes in angle between its ligaments (idealised hinging model). This structure was studied in detail for the potential of exhibiting negative Poisson’s ratio and/or negative compressibility by means of a method based on standard force-field molecular modelling technique, termed as Empirical Modelling Using Dummy Atoms (EMUDA). The mechanical properties obtained from this method were then compared to a previously published analytical model of this structure [Grima J N, CaruanaGauci R, Attard D, and Gatt R 2012, Proc. Roy. Soc. A 468 3121], and found to be in good agreement with each other. The results showed that this system can exhibit zero Poisson’s ratios in one of its planes and positive or negative Poisson’s ratios in other planes, depending on the geometry of the model. It was also shown that under certain conditions, negative linear and/or area compressibility was also exhibited.

Auxetic materials are materials exhibiting a negative Poisson’s ratio in one of their planes. This phenomenon has been studied in various materials. Zeolites are crystalline substances whose structure is characterised by the framework of linked tetrahedra, each consisting of four oxygen atoms surrounding a cation. The resulting interstitial spaces make them efficient for use as adsorbents and molecular sieves, and many studies have been focused on this aspect. Some of these zeolites may exhibit auxeticity at least in one of their planes. THO (and similar systems, such as NAT and EDI) together with the all-silica equivalent of these have been studied extensively via static simulations for their negative Poisson’s ratio in the (001) plane. In this paper a study of the all-silica equivalent of THO has been carried out via both static and dynamic simulations using the same force-field, where the system was subjected to stress along the x direction. The hypothesised semi-rigid mechanism of deformation, proposed by Grima et al. was then projected over this framework. The results obtained confirmed auxeticity along this plane by means of the COMPASS force-field, in both static and dynamic studies and compared well with the proposed mechanism of semi-rigid rotating polygons. It also showed that as the Young’s modulus of this mechanism increases other mechanisms of deformation increase in importance.