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This paper explores how the examination of additively manufactured auxetic componentry can be applied in human-centred design settings with particular focus on biomedical products. Firstly, the design applications of auxetics are detailed followed by a review of the key problems facing practical researchers in the field with the treatment of boundary conditions identified as a key issue. The testing setup that is then introduced utilises a novel method of part mounting and facilitates optical analysis and real-time force–displacement measurements. A study is advanced that analyses three different auxetic structures (re-entrant, chiral, and semi-rigid), a set of samples of which were additively manufactured in flexible TPU material. A range of parameters were varied across the three designs including interior geometry and wall thicknesses in order to demonstrate the effectiveness of the setup for the examination of the different structures. The results from these examinations are subsequently discussed and a number of suggestions made regarding how this kind of analysis may be integrated into novel design development workflows for achieving human-centred biomedical devices which often require detailed consideration of ergonomic and usability factors. [ABSTRACT FROM AUTHOR]

The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson's ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known 'rotating squares' model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed—either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded. [ABSTRACT FROM AUTHOR]

AbstractAuxetics have emerged recently as an exciting class of mechanical metamaterials that are identified by negative Poisson’s ratio. The mechanical properties of rationally designed auxetic metamaterials are mostly influenced by their topological characteristics rather than the material properties of their constituent material. The goal of this paper is to use optimization algorithms to achieve the desired target mechanical properties for reentrant auxetic metamaterials. The GEKKO optimization package in Python is used for optimizing the geometry of auxetic lattice structures. Several mechanical properties including Poisson’s ratio, relative Young’s modulus, relative yield stress, and relative energy absorption capability, as well as the noted properties normalized with respect to relative density and relative Young’s modulus are chosen for being minimized or maximized. ANSYS finite element package is also implemented for validation of the results obtained from the optimization algorithm. According to the results, to achieve the maximum magnitude of Poisson’s ratio (positive and negative), the size of the unit cell in the lateral direction must be selected to be maximum and the thickness must become minimum. Moreover, to achieve the maximum value of the relative Young’s modulus or energy absorption in any direction, the size of the unit cell in that direction must be maximized. Also, to achieve the maximum amount of relative yield stress in both directions, the unit cell must have a maximum thickness and an internal angle close to zero. [ABSTRACT FROM AUTHOR]

This paper aims at to improve the vibration behavior of the train floor panel by the use of a cellular auxetic layer. A field measurement is performed to obtain the vibrational frequency content of the body floor moving on the tangent track. Using acceleration sensors, the vibrational response is measured on the bogie (as the input excitation) and on the floor panel (as the observation response). Finite Element modeling for the floor panel is accomplished and measurement data are used for both the input excitation and the verification of the numerical results. The floor panel is a sandwich panel containing multiple layers. In this study, the conventional wooden layer of the panel is substituted with a cellular auxetic one with a re-entrant hexagonal pattern. Then, an optimization problem is defined while the topological parameters of the auxetic layer are the design variables and the dynamic performance of the panel is the objective function. The parameter of power–mass–ratio (PMR) is defined taking the effects of both weight and dynamic response amplitude into calculation. It is found that the PMR is reduced to almost 0.6 by replacing the wooden layer with an auxetic one, and after topological optimization, it is reduced to 0.35. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents an analysis of a sandwich structure featuring an auxetic core, manufactured through Vacuum Assisted Resin Transfer Molding (VARTM) using carbon-aramid hybrid fibers. The core was 3D printed with polylactic acid (PLA). Experimental testing of the structure provided results for validating a cost-effective numerical model. The response surface methodology identified results for different sandwich panel configurations, revealing that auxetic behavior depends on the core’s adopted configuration. Increasing the fiber-core contact area induces auxetic behaviors. The structure underwent optimization using the Lichtenberg algorithm, yielding models with 40.32% higher failure load, 36.36% higher natural frequency, and over 20% mass reduction. [ABSTRACT FROM AUTHOR]

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]

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Auxetic metamaterials exhibit an unexpected behaviour of a negative Poisson’s ratio (NPR), meaning they expand transversely when stretched longitudinally. This behaviour is generated predominantly due to the way individual elements of an auxetic lattice are structured. These structures are gaining interest in a wide variety of applications such as energy absorption, sensors, smart filters, vibration isolation and medical etc. Their potential could be further exploited by the use of additive manufacturing. Currently there is a lack of guidance on how to design these structures. This paper highlights state-of-the-art in auxetic metamaterials and its commonly used unit-cell types. It further explores the design approaches used in the literature on creating auxetic lattices for different applications and proposes, for the first time, a workflow comprising design, simulation and testing of auxetic structures. This workflow provides guidance on the design process for using auxetic metamaterials in structural applications. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) fabrics with negative Poisson's ratio (NPR) are known as 3D auxetic fabrics. They expand (or contract) in the direction perpendicular to stretch (or compression) under uniaxial tensile (or compressing) conditions. Many enhanced properties come with this unusual auxetic behaviour, such as shear modulus, indentation resistance, fracture toughness, energy absorption, synclastic curvature, etc. Therefore, these 3D auxetic metamaterials have a broad prospect in applications like personal protective equipment as a replacement of polyurethane foams, fabric-reinforced composites with improved ballistic and impact resistance, and women's brassiere paddings with perfect shape-ability. This paper presents a review on 3D fabrics with NPR produced with different fabric technologies, including weaving, knitting, nonwoven, and other techniques. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials have generated considerable interest due to their unique attributes such as light weight, high strength, enhanced energy absorption, high impact, and fracture resistance. However, most of the design methodologies in literature are predominantly computational and provide limited user-insight (especially for three-dimensional designs). This paper presents an alternative two-phase design methodology for the conceptual synthesis of three-dimensional tunable mechanical metamaterials. In the first phase, we obtain a kinematically feasible conceptual topology using a building block-based design approach. In the second phase, the conceptual topology is refined using shape/size optimization to meet specific elastic properties and conform to manufacturing requirements. The building block-based approach uses a unique visualization formulation that represents the deformation behavior as 'load flow' in the constituent members. An immersive virtual reality tool is developed to mitigate the visual difficulty in the design of three-dimensional microstructures. Furthermore, the load flow formulation is used to propose a qualitative classification scheme for negative Poisson's ratio elastic metamaterials based on relative values of shear moduli and bi-axial elastic stiffnesses. The efficacy of the framework is illustrated through the design of microstructures with negative Poisson's ratios in spatial directions and the ability to achieve isotropic microstructures from a qualitative understanding of the conceptual designs. Such a framework can lead to the design of synthetic materials that have potential applications in multifunctional structures, shape morphing structures, and soft robotics. [ABSTRACT FROM AUTHOR]

This paper analyzes the basic geometric and kinematic characteristics of auxetic structures. The geometric principles are then transferred to a family of new possible forms. We investigate and elaborate auxetic behavior in a purely geometric way which is based on the kinematic movement of different frameworks. We then demonstrate its usefulness by analyzing the involved geometry with computer software but without computer simulations or numerical approximations. Instead, using cut flat material and, depending on the cuts and the material used, we enable the kinematical movement of the structures. We also analyze monostable auxetic structures whose movements can be described as geometrically precise, as well as bistable ones. Based on geometric considerations, we combine rigid materials and composites and select appropriate joint connections to allow the application of this system in an architectural scale in, for example, facades, screens or shading systems. [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]

Auxetic structures have unique properties wherein the structure collapses inward in the lateral direction when compressed longitudinally and expands in the lateral direction when subjected to longitudinal tensile load. This paper focuses on improving the impact absorption potential of the arrowhead auxetic structure. Topology optimization is performed on this structure to identify areas in the structure where material reduction is possible. The optimized structure inspired the creation of three new variants of the arrowhead structure. These designs are 3D printed using ABS and PLA materials. Compression and impact tests are performed on a drop test rig and a compression test set-up. From the results, an optimal design is obtained that strikes a balance between compressive strength and impact absorption. In addition, a scope for functional structures that are tailor-made for specific applications, based on a trade-off between impact absorptivity and compressive strength, is identified. [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]

In this paper, a pseudo-rigid body model is proposed for the analysis of a spatial mechanical metamaterial and its application is demonstrated. Using this model, the post-buckling behavior of the mechanical metamaterial can be determined without the need to consider the whole elastic structure, e.g., using finite-element procedures. This is done by analyzing a porous cylindrical mechanical metamaterial using a rigid body mechanism, consisting of rigid squares that are connected at their corners. Stiffness in this model comes from torsion springs placed at the connections between rigid parts. The theory of the model is presented and the results of two versions of this model are compared through experiments. One version describes the metamaterial in the free state, while the other, more extended, version includes clamped boundaries, matching the conditions of the experimental set-up. It is shown that the mechanical behavior of the spatial metamaterial is captured by the models and that the shape of the metamaterial in the deformed state can be obtained from the more extended model. [ABSTRACT FROM AUTHOR]

The paper "Buckling of stretched strips" [1] , published in the year 2000, seemed to deal with a rather specific problem of buckling of thin structures. Nevertheless, it aroused quite broad interest and prompted a considerable series of further treatments. Deeper theoretical considerations and advanced applications have been published. Various specific aspects of this type of problem have been addressed in these papers. However, a general and systematic consideration of how and to what extent the Poisson's ratio affects the critical stretch of strips of different length to width ratios, L / B , was lacking. Accomplishing this task is the focus of this paper. Given the increasing use of auxetics, strips made from such materials are also being investigated. In addition, the occurrence of previously undiscovered mode transitions is shown. All results are presented in dimensionless form, which allows for fairly general usage. • Influence of Poisson ratio on buckling of stretched strips quantified and discussed. • So far unknown mode transition detected and explained. • Buckling of stretched strips made of auxetic materials – diagrams for buckling factor in dependence of Poisson ratio. [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]

• The proposed design exhibits better energy absorption characteristics. • Reinforcing ligaments ensure uniform deformation and improved stability. • The proposed design maintains a constant Poisson's ratio under relatively large deformation. • The theoretical derivation is simple and applicable to other auxetic structures. The traditional anti-tetra-missing rib structure often suffers from uneven stress deformation and poor energy absorption, which limits its engineering applications. To address these limitations, this paper proposed a novel windmill-shaped auxetic structure by incorporating reinforcing ligaments into the traditional anti-tetra-missing rib structure. The incorporation of these reinforcing ligaments ensures that both the outer and inner ligaments of the windmill-shaped auxetic structure are adequately supported, leading to more uniform structural deformation and enhanced energy absorption capabilities. Further modifications, such as reducing the length of the outer and inner ligaments and increasing their thickness within a reasonable range, significantly enhance the energy absorption capacity. These findings provide a theoretical basis for the design and practical application of auxetic metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

Designing a particular change in a system structure to achieve the desired elastic properties of materials for a given task is challenging. Recent studies of purely geometrical atomic models have shown that structural modifications on a molecular level can lead to interesting and desirable elastic properties. Still, the result of such changes is usually difficult to predict. The present work concerns the impact of nanolayer inclusion ordering in hard sphere crystals on their elastic properties, with special attention devoted to their auxetic properties. Two sets of representative models, based on cubic crystals consisting of 6 × 6 × 6 unit cells of hard spheres and containing either neighboring or separated layers of spheres of another diameter, oriented orthogonally to the [001] direction, have been studied by Monte Carlo simulations in the isothermal–isobaric (NpT) ensemble. Their elastic constants have been evaluated using the Parinello–Rahman approach. The Monte Carlo simulations showed that introducing the layer inclusions into a pure face-centered cubic (FCC) structure leads to the system's symmetry changes from cubic symmetry to tetragonal in both cases. Essential changes in the elastic properties of the systems due to layer ordering were found both for neighboring and separated inclusions. It has been found that the choice of a set of layer inclusions allows one to tune the auxetic properties in two crystallographic directions ( [ 110 ] [ 1 1 ¯ 0 ] and [ 101 ] [ 1 ¯ 01 ] ). In particular, this study revealed that the change in layer ordering (from six separated layers to six neighboring ones) allows for, respectively: (i) enhancing auxeticity of the system in the [ 101 ] [ 1 ¯ 01 ] direction with almost loss of auxetic properties in the [ 110 ] [ 1 1 ¯ 0 ] direction in the case of six separated layers, while (ii) in the case of six neighboring layers, keeping the auxetic properties in both auxetic directions independently of the size of spheres constituting inclusions. [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]

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

The 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 deals with a comparative study on the mechanical, acoustic, and electromagnetic properties of a novel class of auxetic (negative Poisson's ratio) rigid polyurethane (PU) foam with a magnetorheological (MR) fluid coating. An auxetic solid expands in all directions when pulled in only one, thus behaving in an opposite manner compared to `classical' solids. When compared with the conventional PU foam, the auxetic PU foam shows enhanced crashworthiness properties and increased sound absorption characteristics (at low frequencies). Samples of auxetic foam coated with MR fluid are examined in this work. While the tensile mechanical properties of the MR fluid-coated samples are affected mainly by surface effects, the acoustic absorption characteristics show almost constant values beyond the cut-off frequency level of the original uncoated auxetic foam. With regard to the foams' electromagnetic properties, the auxetic structure and MR coating cause an increase in the refractive index and loss factor compared to the conventional foams. These electromagnetic effects are due to the presence of a high relative density and metal particulates in the foam material. [ABSTRACT FROM AUTHOR]

A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson's ratio were observed in in situ compression experiments and finite element simulations, suggesting that the mechanical behavior of the hierarchical metastructure is highly ordered and can be programmed by constraining angles of the proposed metamaterial. This work offers new insights to create mechanical metamaterial using hierarchical rotating structures for flexible devices and crashworthiness applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials. [ABSTRACT FROM AUTHOR]

The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson's ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure's linear dimensions and Poisson's ratio. The obtained findings suggest that Poisson's ratio is intricately tied to the structure's opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson's ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson's ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles. [ABSTRACT FROM AUTHOR]

[Display omitted] • Deflection behaviour of existing auxetic re-entrant beams compared with traditional beam designs. • Overlooked factors of placement and orientation of auxetic clusters utilized for enhancement. • Two new improved auxetic beam designs proposed with minimal deflection and 64% reduction in material. • Usefulness of the proposed designs brought out by application into lightweight foot bridge design. Auxetic materials have gained popularity in engineering applications owing to their unique deformation response mechanism. However, they have not been exploited to their full potential in engineering load bearing applications. The current paper, therefore, is focused on exploring and improving the deflection behaviour of auxetic beam structures. Initially, a single re-entrant unit cell and an array of auxetic clusters are modelled using Finite Element Method (FEM). These numerical models are then verified for its Poisson's ratio and deflection behaviour using theoretical formulations. Subsequently, in the next phase, a comparison of the deflection characteristics of the in-use common beams with that of the conventional auxetic beam design is carried out. Much overlooked factors such as orientation and placements of auxetic clusters are introduced in beam designs and are exploited to improve the deflection characteristics of conventional auxetic beams. Through this assessment, the paper proposes two novel design concepts of Oriented Re-entrant Structures (ORS) and Assorted Re-entrant Structures (ARS) for improved load bearing response. Novel designs of ORS and ARS beams are observed to perform significantly better than the conventional auxetic and honeycomb beams. The newly proposed beam designs exhibit a 64% reduction in mass in comparison to the homogeneous beam. The usefulness of these designs are brought out by introducing the ARS auxetic beams into a real-world lightweight foot bridge design. The bridge designs with ARS cross beams demonstrates a better behaviour in comparison to the bridge designs with conventional cross beams in terms of both deformation and material usage. This work highlights the potential use of unconventional mechanical metamaterial structures in engineering load bearing problems to address the demands of green engineering and sustainability without compromising on its structural integrity. [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]

In the present paper, we analyze uniaxial deformation of crystals of different systems with negative Poisson's ratios, known as auxetics. The behavior of auxetic crystals is studied on the basis of extensive knowledge on the experimental values of elastic constants of different crystals, gathered in the well-known Landolt-Börnstein tables. The competition between the anisotropy of crystal structures and the orientation of deformable samples results in the dependence of the elastic characteristics of deformation, such as Young's modulus and Poisson's ratio, on the orientation angles. In the special case of a single angle, a large number of auxetics were found among crystals of cubic, hexagonal, rhombohedral, tetragonal, and orthorhombic systems and the character of variations in their response due to changes in orientation was determined. [ABSTRACT FROM AUTHOR]