Auxetic Behavior Research Articles

Shape-adaptable and wearable strain sensor based on braided auxetic yarns for monitoring large human motions

As one of the flexible and wearable strain sensors, yarn sensors have shown promising applications in monitoring human motions. In this research, shape-adaptable, and wearable braided auxetic yarns (BAYs) sensors were designed and large-scale manufactured by a simple method. The auxetic behavior, mechanical and electrical properties of BAYs were measured and analyzed. The prepared BAYs demonstrated the obvious auxetic behavior (negative Poisson's ratio >-3) and maintained the stability of negative Poisson's ratio performance for long-terms, revealing excellent shape adaptability and structure stability. The auxetic BAYs sensors exhibited a fast response time (149.9 ms), a wide sensing range (0–40.7 %), and excellent cyclic stability. The deformation sensing mechanism of the BAYs sensor was proposed. The fabricated BAYs sensors were directly used to detect and recognize muscle and joint motions, showing outstanding accuracy, stability, repeatability, and shape fitting performance on large curved surfaces (e.g., human body parts like elbow and knee). The excellent performances and auxetic behavior of BAYs sensors would provide remarkable potential in shape-adaptable, flexible, and wearable electronics.

Laser additive manufactured NiTi-based bioinspired helicoidal structure with excellent pseudoelasticity and energy absorption capacity

Functionality-driven biomimetic additive manufacturing (AM), as a research hotspot of 3D printing field, is providing unprecedented opportunities for developing next-generation functional materials in mechanical, electrical, optical and biomedical engineering. In this work, we developed a laser AM-ed NiTi-based helicoidal structure with excellent pseudoelasticity and energy absorption capacity, inspired by the biological architecture in the exoskeleton of the crab's claw. The rotation angle θ corresponding to the misorientation of rods in adjacent layers, as the key structure parameter, was involved into the investigations on the forming quality, pseudoelastic response and fracture behavior of the laser AM-ed helicoidal structures. The results showed that an increase in θ could improve the forming accuracy of rods but decrease the porosity due to the formation of more closed pores filled with unmelted powder particles. These pores formed by the helically stacked rods had sharp edges that could trigger earlier stress concentration and phase transformation or even strain hardening during the loading process. In views of more uniform stress distribution, the helicoidal structure with θ = 36° exhibited the largest recoverable strain of 4.32 %. Regarding the deformation and fracture behavior, it was found that the helicoidal structures with small θ were inclined to exhibit an auxetic deformation behavior and a sluggish fracture process, while the ones with larger θ were prone to a buckling deformation mode and a sudden failure. Furthermore, all helicoidal structures presented excellent energy absorption properties in terms of both unit volume and unit mass values, which could be attributed to the cross-scale hierarchical structures.

Perforated auxetic honeycomb booster with reentrant chirality: A new design for high-efficiency piezoelectric energy harvesting

The present study develops an auxetic meta-structure booster to advance piezoelectric energy harvesting (PEH). The model comprised a three-dimensional (3D) cantilever beam equipped with an auxetic substrate bonded to a piezoelectric (PZT) point defect using an epoxy layer. The substrate used in this proposed energy harvester possesses an auxetic region responsible for generating auxetic behavior and concentrating stress in the PZT layer. The auxetic model called auxetic structure (AS)-II is inspired by ancient motifs and is designed based on the combination of several promising mechanisms, including reentrant, chiral, perforation, and honeycomb supercell. The finite element method is employed to create numerical models whose accuracy is confirmed by mesh convergence and available experimental data. A parametric study is conducted on the AS-II harvester to examine the influence of geometry and PZT material type on the harvested electrical power. Our research efforts stem from both mechanical and electrical circuit fields to fulfill the broadband design target within the desired ultra-low-frequency range of regardless of the resonance condition. As a result, the impact of other factors, such as load resistance, frequency, load amplitude, and bonding stiffness, on the PEH performance is further investigated. The reason behind such outstanding performance of AS-II is explained in terms of geometrical physics and stress distribution. The effect of geometrical dimensions on the auxetic behavior is also analyzed using Poisson’s ratio (PR) study. Subsequently, we demonstrate that this innovative adapter can advance the system’s performance in terms of harvested power and lightweight by a magnification factor of and times that of a plain substrate and and 3.16 times that of a conventional auxetic harvester, respectively. The present harvester is strain controllable, where it can set PR between and resulting in robust PEH even if switching input vibration from high to low levels. This new idea enables us to serve cantilever-type resonators at frequencies far lower than their resonant frequencies with small portions of incident excitement.

Auxetic and Non‐Auxetic Metamaterial Model from Interconnected Rotating Parallelograms and Triangles

This article reports the design of a metamaterial model—made from interconnected units of rotating parallelograms and triangles—in which its Poisson's ratio can range from positive to negative by changing the internal angles between the rotating units. The on‐axes Poisson's ratios are established via geometrical construction while the on‐axes Young's moduli are extracted using energy approach. Results indicate that the metamaterial model manifests auxetic behavior for small and large internal angles, but non‐auxetic properties for intermediate range of internal angle. The results also reveal that a wide range of on‐axes Young's modulus can be adjusted by controlling the internal angle. A sustainable feature of this metamaterial model is its convenient adjustment of the effective mechanical properties over a wide range in order to be redeployed for different applications throughout its entire lifetime.

Excitonic effects on the optical spectra of TiB2 nanosheets

Two-dimensional (2D) transition metal borides, have recently attracted tremendous interest and become an emerging class of 2D materials due to their intriguing properties. We report systematic investigation of stability, electronic properties and optical activity of 2D-TiB2 nanosheets using first-principles calculations. By combining elastic and phonon-dispersion calculations, we substantiated the mechanical and dynamic stability of 2D-TiB2 nanosheets. Our results of elastic calculations reveal that addition of an extra layer destroys the auxetic behaviour of monolayer (ML) 2D-TiB2 with significant reduction in the brittleness. Further, based on the spin-polarised electronic structure calculations, we find that a low-dimensional metallic state of ML can be achieved by tuning the distance between the titanium and boron layers. The calculations clearly reveal that metallic nature does not destroys the auxetic behaviour of ML. Subsequently, we investigated the optical response of 2D-TiB2 nanosheets (ML and bilayer (BL)) at the level of density functional theory and many-body perturbation theory. The results obtained by solving Bethe–Salpeter equation (GW+BSE formalism) shows that excitonic effects causes a slight blue-shift in the absorption spectra of the nanosheets with ML being optically active with sharp peaks in infrared (IR) and ultraviolet (UV) regions while BL shows the reduced optical activity across wide range of photon energies spanning the near-IR to UV region. In addition, electronic polarisability of the nanosheet decreases with addition of another layer in ML 2D-TiB2. Further investigation of transition probabilities clearly indicates that the response of ML at Dirac point is tunable by spin–orbital coupling effects which makes these nanosheets promising for spintronic applications. The BL exhibits distinct electronic, and optical properties compared to ML. Our study unravels the structural, elastic, electronic, and optical properties of 2D-TiB2 nanosheets and suggests them as promising candidate for variety of optoelectronic and spintronic applications.

Tensile Mechanical Behaviors of Re-entrant and Kelvin Cell Lattice Structures

Periodic lattice structures as lightweight and high-energy absorption materials have been widely used in various fields, among which re-entrant and Kelvin cell lattice structures have exhibited excellent mechanical behaviors under different loadings. Therefore, this study aims to numerically explore and compare the tensile mechanical responses of re-entrant and Kelvin cell lattice structures with the same relative density after validating with experimental tests. It has been found that the tensile behavior of the two stretching-dominated lattice structures resemble that of parent solid material but had smaller fracture stress and strain due to the lower ductility of the lattice structures. The re-entrant lattice structure displayed a better energy absorption capacity than the Kelvin cell lattice under tensile loading, i.e., the energy absorption and specific energy absorption of the re-entrant lattice were 3 times and 1.6 times, respectively, those of the Kelvin cell lattice. Meanwhile, the re-entrant lattice as expected exhibited auxetic behavior with a negative Poisson’s ratio during the whole stretching process, while the Kelvin cell had the mechanical behaviors of traditional materials with a relatively constant positive Poisson’s ratio. These results are expected to provide hints on mechanical references and guidance for their extensive applications in the future.

A simulation approach to auxetic and non-auxetic behavior of 3D composites produced with multi-cell flat-knitted spacer fabrics

The paper aims to simulate the auxetic and non-auxetic behavior of 3D composites reinforced with multi-cell flat-knitted spacer fabrics. Spacer weft knitted preforms were fabricated on an electronic flat knitting machine. 3D knitted composite samples with re-entrant, regular hexagonal and spear-head geometries, were prepared via vacuumed assisted resin transfer molding method. Using a cross-over geometrical model surrounded by a rigid resin cube, the composite unit-cell was designed in Abaqus software’s environment. Chamis micromechanical model was then used to determine the elastic constants of composite unit-cell. Meso-macro finite element analysis was used to simulate the response of the 3D composites to compressive loading. The results revealed that the Poisson’s ratio of re-entrant and hexagonal 3D knitted composite varied between −6 and −1 and 1.6 to 3.8, respectively. Also, the Poisson’s ratio of spear-head knitted composite was measured as zero. The proposed model was used to verify the predicted compressive behavior and Poisson’s ratio of the prepared composite samples. For hexagonal knitted composite, the proposed model demonstrated a good agreement with the experimental results. The Poisson’s ratio-strain curve obtained for 3D re-entrant knitted composite is highly compatible to those due to modelling results in strain range of about 5.8 to 22.5%. Also, for 3D spear-head knitted composite, the modelling results are not compatible to experimental method at strain values over 6%.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

Composites with Re-Entrant Lattice: Effect of Filler on Auxetic Behaviour.

This study is focused on the deformation behaviour of composites formed by auxetic lattice structures acting as a matrix based on the re-entrant unit-cell geometry with a soft filler, motivated by biomedical applications. Three-dimensional models of two types of the auxetic-lattice structures were manufactured using filament deposition modelling. Numerical finite-element models were developed for computational analysis of the effect of the filler with different mechanical properties on the effective Poisson's ratio and mechanical behaviour of such composites. Tensile tests of 3D-printed auxetic samples were performed with strain measurements using digital image correlation. The use of the filler phase with various elastic moduli resulted in positive, negative, and close-to-zero effective Poisson's ratios. Two approaches for numerical measurement of the Poisson's ratio were used. The failure probability of the two-phase composites with auxetic structure depending on the filler stiffness was investigated by assessing statistical distributions of stresses in the finite-elements models.

Negative Poisson’s Ratios of Layered Materials by First-Principles High-Throughput Calculations

Auxetic two-dimensional (2D) materials, known from their negative Poisson’s ratios (NPRs), exhibit the unique property of expanding (contracting) longitudinally while being laterally stretched (compressed), contrary to typical materials. These materials offer improved mechanical characteristics and hold great potential for applications in nanoscale devices such as sensors, electronic skins, and tissue engineering. Despite their promising attributes, the availability of 2D materials with NPRs is limited, as most 2D layered materials possess positive Poisson’s ratios. In this study, we employ first-principles high-throughput calculations to systematically explore Poisson’s ratios of 40 commonly used 2D monolayer materials, along with various bilayer structures. Our investigation reveals that BP, GeS and GeSe exhibit out-of-plane NPRs due to their hinge-like puckered structures. For 1T-type transition metal dichalcogenides such as MX 2 (M = Mo, W; X = S, Se, Te) and transition metal selenides/halides the auxetic behavior stems from a combination of geometric and electronic structural factors. Notably, our findings unveil V2O5 as a novel material with out-of-plane NPR. This behavior arises primarily from the outward movement of the outermost oxygen atoms triggered by the relaxation of strain energy under uniaxial tensile strain along one of the in-plane directions. Furthermore, our computations demonstrate that Poisson’s ratio can be tuned by varying the bilayer structure with distinct stacking modes attributed to interlayer coupling disparities. These results not only furnish valuable insights into designing 2D materials with a controllable NPR but also introduce V2O5 as an exciting addition to the realm of auxetic 2D materials, holding promise for diverse nanoscale applications.

Numerical investigation of the Poisson's ratio of amorphous graphene sheets

AbstractThe one‐atom‐thick allotrope of graphite, C4 is called monolayer graphene and was discovered in 2004. It is well known for its fantastic electro‐mechanical properties. While transverse contraction and Poisson's ratio were previously studied only for homogeneous or crystalline two‐dimensional (2D) mono‐ and bilayer network structures under uniaxial tensile stress, we now numerically investigate these material properties for amorphous or non‐crystalline monolayer graphene. Here, we pay special attention to the influence of the network heterogeneity. We find the stress‐strain correlation in good agreement with the literature, and we find auxetic behavior, that is, negative Poisson's ratio, over a wide range within the elastic regime.

A star-shaped tubular structure with multiple-directional auxetic effect

A majority of tubular structures have been widely studied due to their superior mechanical performance. Existing works on star-shaped tubular structures have focused on improving their stability and energy absorption performance. This paper proposes a novel star-shaped tubular lattice structure (STL), which not only possesses excellent mechanical properties but also exhibits exceptional auxetic effect. In addition, such structures exhibited two distinct deformation modes under different loading directions. Numerical and experimental studies of the mechanical behavior of the star-shaped tubular structure demonstrated low peak stresses under lateral loading and superior bearing capacity and stability under axial compression. Most importantly, the structure embodied a significant auxetic effect under the direction of both loads. The mechanical performance of the star-shaped tubular structures was investigated by changing wall thickness and angles, which can realize the optimal design. This study enriches the research on star-shaped tubular structures and provides a new perspective and reference for the design of auxetic tubular metamaterials in the future. Furthermore, the star-shaped tubular structure with auxetic behavior has considerable potential for applications in civil engineering and protective fields.

A NOVEL YARN FOR PERSONEL PROTECTION IN KNITTED SPORTSWEAR

In the textile and clothing sector, a wide range of auxetic textiles have been made and shown great application potential in many areas. Creating auxetic effect at the yarn stage is relatively a simple approach since helical auxetic yarns (HAY) can be made only by winding or twisting different conventional filaments together with existing spinning machinery. Employing sports safety equipment is a cost-effective solution for avoiding injury and increasing the safety and protection. In the area of materials development for sports safety equipment, an important candidate is auxetic materials. In this study, polyester filament/elastane based helical auxetic yarns (HAY) and knitted fabrics from the yarns were developed that will offer dampening effect against injuries during sports activities. Effects of count of the elastane component and the presence of a third component in the HAY structure on the auxetic behaviour of the knitted fabrics were also studied.

Triply periodic minimal surfaces lattice structures: Functional graded and hybrid designs for engineering applications

In this work, we propose the strategies for designing radial graded sheet-based gyroid lattice and the approach to hybridizing solid-network-based gyroid lattice and primitive lattice. The elastic property of triply periodic minimal surfaces (TPMS) sheet-based gyroid lattice structures was explored. We also conducted numerical analysis to investigate the effect of functionally graded sheet-based gyroid lattices on the implant application, and explored the elastic properties of the uniform gyroid lattice parametrically with different relative densities based on the representative volume element model. Analytical equations based on the Gibson-Ashby model were generated to predict the elastic properties. Compressive tests on the samples fabricated by the Stratasys J750 were conducted to validate the feasibility of applying hybridization of different types of lattices. A comparison between radial hybrid primitive-gyroid and gyroid-primitive lattices revealed that the compressive behavior of gyroid-primitive was strengthened. We also found that the gyroid-primitive lattice could achieve auxetic compressive behavior. In conclusion, the numerical analysis illustrates that the application of the functional graded gyroid lattices can relieve the stress shielding effect as well as protects the bone from damage. The hybridization of different lattices can not only strengthen the mechanical properties of TPMS structures but also create a counter-intuitive deformation response.

Polybutylene Succinate Auxetic Membrane Produced by Solution Electrospinning

Herein, a simple and cost‐effective method (solution electrospinning) is used to produce auxetic biobased polybutylene succinate membranes. The effect of fiber morphology, orientation, and alignment is investigated on the mechanical properties of the resulting membranes with a focus on Poisson's ratio. The degree of orientation is controlled by increasing the speed of the collector (from 4.03 to 11.01 m s−1) during membrane fabrication. The results indicate that membranes with oriented fibers show a more auxetic behavior than those with randomly orientated fibers. In particular, samples with a high level of alignment and tested in the transverse direction present higher negative Poisson's ratios (down to −5.73) compared to samples tested in the parallel direction (Poisson's ratios down to −2.90). However, samples tested in the transverse direction show lower tensile properties with higher dissipated energy and damping factor. Therefore, the level of fiber orientation and the number of fibers in the transverse and parallel directions are the most important parameters controlling the mechanical properties of electrospun membranes.

Compressive Mechanical Behavior of Additively Manufactured 3D Auxetic Metamaterials with Enhanced Strength

Compared with 2D auxetic metamaterials, 3D auxetic metamaterials present better structural, mechanical, and functional properties, which are more applicable in many potential applications in engineering fields. Herein, three types of 3D star‐shaped auxetic (SSA) structures, re‐entrant and star‐shaped composite auxetic (RSA) structures, and star‐rhombic auxetic (SRA) structures with small unit cell are proposed and fabricated by selective laser melting method. The compressive behavior and energy absorption of the auxetic structures are explored and compared based on finite‐element method (FEM) verified by the compression test results of the sample. Meanwhile, the numerical results present good agreements with the experimental results in terms of deformation mode, Poisson's ratio, and compression behavior. The results reveal that SRA structures exhibit superior elastic modulus, compressive strength, and energy absorption than SSA and RSA structures, which stems from the auxetic effect, obstruction of rhombic structures to the deformation of inclined struts and more plastic hinges. It is precisely because of the obstruction of rhombic structures that SRA structures exhibit weakening auxetic characteristic and even no auxetic behavior during the higher strain range. In addition, the length of the structural strut presents a significant impact on the energy absorption performance and compression strength of all the structures.

Molecular Auxetic Polymer of Intrinsic Microporosity via Conformational Switching of a Cavitand Crosslinker

AbstractAuxetics are materials characterized by a negative Poisson's ratio (NPR), an uncommon mechanical behavior corresponding to a transversal deformation tendency opposite to the traditional materials. Here, the first example of a synthetic molecular auxetic polymer obtained by embedding a conformationally expandable cavitand as a crosslinker into a rigid polymer of intrinsic microporosity (PIM) is presented. The rigidity and microporosity of the polymeric matrix are pivotal to maximizing the expansion effect of the cavitand that, under mechanical stress, can assume two different conformations: a compact vase one and an extended kite form. The auxetic behavior and the corresponding NPR of the proposed material is predicted by a specific micromechanical model that considers the cavitand volume expansion ratio, the fraction of the cavitand crosslinker in the polymer, and the mechanical characteristics of the polymer backbone. The reversible auxetic behavior of the material is experimentally verified via the digital image correlation technique performed during the mechanical tests on films obtained by blending the auxetic crosslinked polymer with pristine PIM. Two specific control experiments prove that the mechanically driven conformational expansion of the cavitand crosslinker is the sole responsible for the observed NPR of the polymer.

Auxetic materials and structures for potential defense applications: An overview and recent developments

Auxetic behavior is a promising new area for use in defense applications. In comparison to a conventional material, an auxetic material has superior properties because of having a negative Poisson’s ratio; it gets broadened when stretched or becomes smaller when compressed. Furthermore, auxetic materials have enhanced properties such as shear resistance, indentation resistance, fracture toughness, energy absorption, and so on. These improved properties make auxetic materials very appealing and have the potential to revolutionize their applications in aerospace, sports, automotive, construction, biomedical engineering, smart sensors, packaging, cushioning, air filtration, shock absorption and sound insulation, and defense personal protective equipment. This article examines the most recent scientific advances in auxetic materials and structures, such as auxetic textiles (fibers, yarns, and fabrics), auxetic textile-reinforced composites, and auxetic foams, as well as their exceptional auxetic behavior and various approaches to achieving them. Although many potential applications have been proposed, actual applications of auxetic materials in defense are still limited. This is an in-depth review article, and its main goal is to serve as a foundation for future studies concerning the topic.

Mechanical modelling of viscoelastic hierarchical suture joints and their optimisation and auxeticity

It has been widely recognised that suture joints play a fundamental role in the exceptional mechanical properties of many biological structures like the cranium and ammonite fossil shells. Up to date, many efforts have been devoted to investigate suture interfaces to predict the relations between the characteristics of its two phases, the teeth and the interface layer, and the structure effective properties. However, in very few works the viscoelasticity of the suture components has been taken into account. To provide a contribution in this limitedly explored research area, this paper describes the mathematical formulation and modelling technique leading to explicit expressions for the effective properties of viscoelastic suture joints with a general trapezoidal waveform. It emerges a strong influence of the suture geometric and mechanical characteristics on the effective properties and a parametric analysis reveals that an auxetic behavior can be obtained simply by tailoring the suture parameters. The effects of adding hierarchy into the above system are also explored and closed-form relations for the effective moduli are derived. Optimal levels of hierarchy can be identified and, similarly to the non-hierarchical case, an auxetic behavior emerges for particular values of the suture parameters. Finally, an extension of the theory to the sinusoidal sutures in biology is reported. By considering the examples of the cranium and the woodpecker beak, it emerges that the first is optimised to obtain high stiffness, while the second to obtain high energy dissipation levels.

Insights into the auxetic behavior of graphene: A study on the temperature dependence of Poisson's ratio and in-plane moduli

Graphene is a highly versatile material with many potential applications. Accurately measuring its mechanical properties, especially Poisson's ratio, has been a significant challenge. Computational methods such as Molecular Dynamics and Monte Carlo have been used to estimate this parameter for free-standing samples. However, many studies underestimate details of local geometrical changes, leading to inaccurate results. Here, we use a Discrete Differential Geometry approach to compute local strains from atomic locations found using Molecular Dynamics simulations of graphene samples deformed in simple tension up to an axial strain of 3% at temperatures between 10 and 600 K. We find that the Poisson's ratio at zero external stress/strain at T = 100 K (600 K) equals −0.557 (−0.601) that has not been widely reported in the literature. However, at T = 10 K, Poisson's ratio equals 0.221. We also show that this auxetic behavior is accompanied by the condition μ/B > 1 between the in-plane shear (μ) and bulk (B) modulus. Moreover, graphene's in-plane Young's modulus at T = 300 K and zero axial strain, Y0 ∼ 200 N/m, is significantly less than the commonly reported experimental value, Y0 = 340 N/m. We also delineate the dependence upon the axial strain and the temperature of the Poisson's ratio and the in-plane modulus. These findings have important implications for developing graphene-based materials and devices.