Auxetic Materials Research Articles

In Situ X‐Ray Tomography of Sintered Metal Fiber Felts Exhibiting Auxetic Effect under Tension and Compression

Sintered metal fiber felts (SMFFs) are kinds of the strongest auxetic materials to date, but there are significant differences in the reported auxeticities, due to the lack of investigation on the fabrication process. This study is performed to analyze the influence of fabrication process and structural features on the auxetic effect exhibited by SMFFs. The sequence of compression and sintering processes determines the volume density of the interfiber-sintered joints and the resulting Poisson's ratio behavior under tension and compression. The SMFFs with a low volume density exhibit strong auxetic effect under tension and achiev a positive Poisson's ratio under compression because of the weak interfiber layer bonding. In contrast, the felts with a high density of interfiber joints reveal a relatively weak auxetic effect under both tension and compression. Moreover, an increase in the thickness and a decrease in the porosity reduce the auxetic effect. In addition, in situ X-Ray tomography of the tensile testing is performed to elucidate the mechanism of the auxetic effect. To explain the observed Poisson's ratio behavior under tension and compression, periodical finite-element modeling with real mesostructures is performed. Herein, a new insight into the relationship between the structure features and the Poisson's ratio behaviors is given.

Research on the auxetic behavior and mechanical properties of periodically rotating graphene nanostructures

Abstract Negative Poisson’s ratio (auxetic) material is one of the most widely studied metamaterials, and recent attempts have been made to discover auxeticity in graphene-based and related carbon-based materials. However, it is shown that negative Poisson’s ratio effect requires special conditions, such as high temperature. Achieving negative Poisson’s ratio effect under large strain at ambient conditions is the key to graphene materials in nano-device applications. In order to discover the auxetic properties of nanostructures under large strain, this article proposes periodically rotating graphene nanostructures (PRGNs) which are the combination of graphene and rotating rigid unit structures. Poisson’s ratio, Young’s modulus, and damage mechanism of PRGNs are investigated using molecular dynamics simulation. It can be possible to conclude that PRGNs can also exhibit auxetic behavior, and their negative Poisson’s ratio effect can be maintained even at large strains (ε ∼ 0.1). Poisson’s ratio can be regulated by adjusting the value of the geometry parameters of the graphene sheets (GSs), which comprise the PRGNs, and changed from negative to positive and from positive to negative. Also, the influences of the structural size of GSs and the connection angle between GSs on the mechanical properties are explored, which will provide a theoretical basis for the preparation and performance optimization of GSs and the nano-auxetic properties of materials.

Design and mechanical characteristics of auxetic metamaterial with tunable stiffness

Auxetic materials are a class of mechanical metamaterials. They exhibit lateral expansion under tension, and lateral contraction under compression. Such metamaterials have attracted increasing attention due to their unusual mechanical behavior and various potential applications. However, the stiffness of auxetic structures is much weaker than that of solid ones due to their porous structure. Therefore, many researchers try to enhance the stiffness of auxetic cellular structures to broaden their potential applications. In this study, re-entrant unit cells with different variable stiffness factors (VSF) were designed to achieve the tunability of stiffness from the aspect of tuning the densification strain. Experimental and numerical analyses were carried out to verify the accuracy between the designed and the actual VSF. It is found that the compaction points of the proposed re-entrant structures could be tuned quantitatively using the defined VSF, which provides a new method for the optimal design of negative Poisson's ratio unit cell.

Investigation of Modified Auxetic Structures from Rigid Rotating Squares.

Auxetic structures exhibit unusual changes in size, expanding laterally upon stretching instead of contracting. This paper presents this effect in a failsafe mode in structures made of rigid squares. We applied the concept of auxetic structures made of rigid rotating squares (from Grima and Evans) and offer a novel solution for connecting them. By introducing axes of rotation on the surface of the squares, a reliable working system is obtained, free from stress, in which the squares can come into contact with each other and completely cover the surface of the structure, or, in the open position, form regularly arranged pores. Herein, we present a new 2D auxetic metamaterial that is mathematically generated based on a theoretical relationship of the angle between the edges of a square and the position of the axis of rotation. Physical models were generated in the form of a planar structure and in the form of a circular closed structure. Such physical models confirmed our initial considerations and the geometrical relationships, offering new application possibilities. The novel structure that was designed and manufactured for the purpose of the paper can be considered as a new proposal in the market of auxetic materials.

Proposed auxetic cluster designs for lightweight structural beams with improved load bearing capacity

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.

Tunable compression-torsion coupling effect in novel cylindrical tubular metamaterial architected with boomerang-shaped tetrachiral elements

Manipulation of cellular cylindrical tubes offers great opportunity to design functionalized materials and structures. In this study, inspired by the deformation mechanism of 2D perforated auxetic materials with peanut-shaped cuts, a new design for improving compression-torsion coupling (CTC) performance of tubular mechanical metamaterial is presented by introducing boomerang-shaped tetrachiral elements with curved ligaments, no longer limited to inclined straight ligaments. Static compression experiment and finite element simulation for the fabricated specimen by 3D printing reveal that the specimen exhibits promising CTC performance and the experimental results agree well with the numerical solutions. Moreover, the rotation angle of the tube approximately linearly increases with the increasing compression strain, except for the initial loading stage. Subsequently, the deformation mode of the present CTC tube is further illustrated by comparing to the existing CTC tubes including inclined straight ligaments. The curved ligament in the present design brings more flexible deformation than the straight one, and thus leads to better CTC property. Finally, the effects of controlling parameters on the CTC deformation are comprehensively analyzed to provide a deep understanding of the tunable design of compression-torsion tubular metamaterials for potential applications.

C3Al: A tunable bandgap semiconductor with high electron mobility and negative Poisson’s ratio

Two-dimensional materials with suitable band gaps and high carrier mobility are considered to be ideal for fabricating next-generation microelectronics devices. In this paper, the C 3 Al crystal structure, electronic and mechanical properties are systematically investigated based on a first-principles method. We find that C 3 Al is an auxetic semiconductor material with wide band gap and high carrier mobility. Electrons have good transport properties but holes are almost completely scattered in the zigzag direction. C 3 Al is one of the few materials with negative Poisson’s ratio effect. In addition, the electronic properties of C 3 Al can transform from semiconductor to metal by tuning straining and stacking. The bare-edge and H-terminated C 3 Al nanoribbons shows an enriched set of electronic properties of semiconductors, half-semiconductor, bipolar magnetic semiconductors , non-magnetic metals, magnetic metals, and half-metals. These results not only provide a theoretically novel and promising crystal configuration, but also further explore the potential of the material for applications in biosensing, strain sensors, transistors, and various nano-optical devices. • The C 3 Al has excellent performance in terms of structural and thermodynamic stability. • C 3 Al is an auxetic semiconductor material with wide band gap and high carrier mobility. • The electronic properties of C 3 Al can transform from semiconductor to metal by tuning strain and stacking. • The bare-edge and H-terminated C 3 Al nanoribbons show an enriched set of electronic properties.

Two-dimensional auxetic pentagonal materials as water splitting photocatalysts with excellent performances

Two-dimensional auxetic pentagonal materials as water splitting photocatalysts with excellent performances

Performance analysis of socks produced by auxetic yarns for protective applications

The present work reports application of auxetic yarns in development of abrasion resistant socks which can be used for better serviceability without shoes even on rough surfaces. Socks used in the current research were produced by using helical auxetic yarns which consist of different combinations of high performance and conventional materials e.g. Kevlar P-AR (para-aramid), cotton, elastomeric yarn, polyamide (PA6) and polyester with same linear density of 74 Tex. Three different types of fabrics were produced e.g. flat knit, sandwich half terry short and sandwich half terry long. For investigating the auxeticity, all samples were subjected to tensile loading and the resulting change in their thickness was measured. Abrasion resistance and other comfort related properties e.g. air permeability, vertical wicking and absorbency were also evaluated. The influence of different yarn combinations, twist levels and fabric types on abrasion resistance and breathability of socks were investigated by using fractional (half) factorial design. Statistical analysis was performed for the obtained results by using analysis of variance. Conventional socks samples were also produced in all fabric types for comparison with the auxetic materials. From the results it was concluded that the overall abrasion resistance of auxetic yarn-based sock is higher than conventional cotton sock. Results also revealed that abrasion resistance was increased by 46% in flat knit socks sample, 50% in sandwich half terry short sample and 58% in sandwich half terry long sample as compared to conventional cotton sock. In addition to this all the socks samples exhibited good comfort/breathability properties.

Appearance of Supersonic Stoneley Waves in Auxetics

It is shown that in auxetic materials (materials with negative Poisson’s ratio), supersonic Stoneley waves travelling without attenuation with a velocity equal to or exceeding maximum bulk wave velocity, may exist. Analytical expressions for the relation between negative Poisson’s ratio and Young’s moduli of the contacting isotropic media ensuring the condition of propagation for supersonic Stoneley waves, are derived by solving a secular equation for Stoneley waves.

Recent advances in auxetics: Applications in cementitious composites

Auxetic materials, possessing negative Poisson’s ratios (NPRs), have the ability to shrink (or expand) in the lateral direction under an axial compressive (or tensile) force respectively. Due to this unique feature, an auxetic material is found to sustain high energy absorption capacity, fracture toughness and shear resistance and thus regarded as one of the future materials in the field of impact protection. However, civil engineering applications of auxetic structures or materials are minimal due to miscellaneous restrictions on NPR effects. Accumulative developments in auxetics have facilitated their applications in cementitious materials in recent years. This paper presents an overview of recent advances in the development of auxetic cementitious composites and analyses and summarises their mechanical properties under different loading conditions. Prior to extensive finite element simulations, more attention has been given to the limited experimental results. Particular attention is paid to the expansionary feasibility of the parent material to introduce auxetic behaviour, with precise identification of the limitations, innovative composition methods and facilitation of auxetic features. Finally, the paper outlines the limitations of the current research and envisages few future research opportunities in auxetic cementitious composites.

Mechanical properties and fracture analysis of defective penta-graphene under temperature variation: Insight from molecular dynamics

Classical molecular dynamics simulations have been performed to investigate five mechanical properties of defective penta-graphene under uniaxial tension, namely Young's modulus, Poisson's ratio, ultimate tensile stress, ultimate strain, and toughness. The reliable Erhart-Albe formulation of the Tersoff potential has been used in the simulations and monovacancies are the only kind of structural defect studied. The effects of defect density, chirality, and temperature on the mechanical properties are reported and thoroughly discussed. The results show that by incorporating defects up to 20%, Young's modulus is decreased by more than one order of magnitude and the sign of the mean Poisson's ratio changes to positive, which indicates the possibility of tuning this ratio. Furthermore, the anisotropic behavior of the material is not strong in terms of Young's modulus, ultimate stress, and ultimate strain and at higher temperatures, the ultimate stress, ultimate strain, and toughness almost converge for pristine and defective penta-graphene. It can be concluded that PG is an auxetic material while it can be tuned by defect engineering to behave as classic material. It should be noted that the results of current study can be used as benchmark for design and fabrication of novel potential industrial materials with both negative and positive Poisson's ratios.

Elasticity of Nonstoichiometric Alumina-Rich Spinel Determined by Bond Valence Theory and Brillouin Scattering.

An accurate knowledge of the elastic properties of materials is essential for material science and engineering applications. Four single crystals of nonstoichiometric alumina-rich spinel [Mg1-xAl2(1+x/3)O4] were obtained from sintered transparent ceramics for the investigation of its elastic properties. The disordered crystal structures were fully resolved by combining single-crystal structure refinement and a quadratic programming approach for the first time. The bond valence model and Brillouin scattering experiments were used to evaluate the bulk modulus (K), shear modulus (G), Young's modulus (E), and Poisson's ratio. The discrepancy between the theoretical and experimental results is <2.6%. The independent elastic constants (C11, C12, and C44) were determined from Brillouin scattering experiments. A negative Poisson's ratio, υ(110, 11̅0), was found to exist in all alumina-rich spinels, which means it is a partially auxetic material. Blackman diagram analysis was introduced to identify the interrelationships and trends in mechanical and bonding properties in alumina-rich spinels. The bond valence model was suggested to be an effective and accurate approach for predicting the elastic modulus of spinels, which provides a useful tool for the study of the composition-structure-property relationship of materials.

Extremely stiff and lightweight auxetic metamaterial designs enabled by asymmetric strut cross-sections

Negative Poisson’s ratio has been shown to enhance packing efficiency, impact absorption, indentation resistance, fracture resistance and acoustics attenuation in auxetic materials, making them useful for applications such as protective cases and stents. However, these benefits are usually realized at the expense of a low specific modulus and poor loading efficiencies, as auxetic structures rely on ‘soft’ strut bending and/ or joint rotation deformation modes to reach perceptible levels of negative Poisson’s ratios. Here, a general 3D Anti-Tetrachiral (3ATC) structure was analyzed and shown that, in the limit of low relative density (i.e lightweight structure), the trade-off between specific relative stiffness and auxeticity is linear and the maximum attainable specific relative stiffness is 1/3. If the strut cross-section is symmetric, the maximum attainable Poisson’s ratio is -0.5, while that for an asymmetric cross-section depends on the specific geometry of the cross-section. Importantly, our analysis shows that the non-zero product of inertia for asymmetric cross-sections can lead to an additional twist of the joint, thereby increasing the auxeticity of the 3ATC structure. This allows the 3ATC lattice to exhibit a large specific relative stiffness for a given Poisson’s ratio, which can be more than an order of magnitude higher when compared to other auxetic designs in the literature. Our analysis was validated by finite element simulations and experiments on 3ATC lattices with strut cross-sections that were square (symmetric) and L-shaped (asymmetric).

Design and Characterization of Asymmetric Cell Structure of Auxetic Material for Predictable Directional Mechanical Response.

A three-dimensional auxetic structure based on a known planar configuration including a design parameter producing asymmetry is proposed in this study. The auxetic cell is designed by topology analysis using classical Timoshenko beam theory in order to obtain the required orthotropic elastic properties. Samples of the structure are fabricated using the ABSplus fused filament technique and subsequently tested under quasi-static compression to statistically determine the Poisson’s ratio and Young’s modulus. The experimental results show good agreement with the topological analysis and reveal that the proposed structure can adequately provide different elastic properties in its three orthogonal directions. In addition, three point bending tests were carried out to determine the mechanical behavior of this cellular structure. The results show that this auxetic cell influences the macrostructure to exhibit different stiffness behavior in three working directions.

2D Janus and non-Janus diamanes with an in-plane negative Poisson's ratio for energy applications

Motivated by the successful synthesis of 2D C2F diamanes [Bakharev, P.V. et al., Nat. Nanotechnol. 15, 59–66 (2020)], we have systematically investigated the structural stability, in-plane mechanical, optoelectronic, photocatalytic, piezoelectric, and thermoelectric properties of non-Janus and Janus diamanes monolayers named as C2H, C2F, C2Cl, C4HF, C4HCl and C4FCl. The structural stability is confirmed by cohesive energy, phonon dispersion spectra, and mechanical properties. The electronic properties has been calculated by HSE06 functional and the band gap are found to be 3.85, 5.64, 2.32, 4.16, 0.73 and 1.91 eV for C2H, C2F, C2Cl, C4HF, C4HCl and C4FCl, respectively. The hydrogen-containing non-Janus and Janus diamanes monolayers have a higher negative Poisson's ratio (NPR) and therefore are good auxetic materials. From the Poisson's ratio and Young's modulus of each configuration of non-Janus and Janus diamanes monolayer, anisotropic behavior was displayed. From the optical properties calculations, the refractive index values are around 1.5, which means that it will be a transparent monolayered materials. Also, C2Cl, C4HCl and C4FCl monolayers displayed high absorption spectra with an order of 105 cm−1 in the visible region, which shows great applications in optoelectronic devices. Additionally, the valence and conduction band-edge positions of 2D Janus and non-Janus diamanes of C2H, C2F, and C2Cl and C4HF monolayers have to straddle the redox potentials of water. It means that the photogenerated electrons and holes are sufficient to drive the overall water splitting. Whereas non-Janus diamanes C4HCl, and C4FCl monolayers displayed only water oxidation. The investigated in-plane piezoelectric coefficient has larger in non-Janus diamanes C4HF, C4HCl, and C4FCl monolayers. Therefore, it is very useful in the field of piezoelectric applications. From the thermoelectric properties, the non-Janus and Janus diamanes monolayers have great thermoelectric efficiency and were found to be 10.52 and 10.63% for C2H and C2F, respectively. Our results demonstrate the new class of 2D carbon-based monolayers has good auxetic materials as well as a wide range of applications in optoelectronics, piezoelectric, and thermoelectric fields.

Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

If a conventional material is compressed in one direction, it tries to expand in the other two perpendicular directions and vice versa, indicating a positive Poisson's ratio. Recently auxetic materials with negative Poisson's ratios, which can be realized through artificial microstructuring, are attracting increasing attention due to enhanced mechanical performances in multiple applications. Most of the proposed auxetic materials show different degrees of in‐plane auxeticity depending on their microstructural configurations. However, this restricts harnessing the advantages of auxeticity in 3D systems and devices where multidirectional functionalities are warranted. Thus, there exists a strong rationale to develop microstructures that can exhibit auxeticity both in the in‐plane and out‐of‐plane directions. Herein, generic 3D connected double loop (3DCDL) type periodic microstructures are proposed for multi‐directional modulation of Poisson's ratios. Based on the bending dominated behavior of elementary beams with variable curvature, mixed‐mode auxeticity following the framework of multimaterial unit cells is demonstrated. The proposed 3DCDL unit cell and expanded unit cells formed based on their clusters are capable of achieving partially auxetic, purely auxetic, purely nonauxetic and nullauxetic behavior. Comprehensive numerical results are presented for the entire spectrum of combinations concerning the auxetic behavior in the in‐plane and out‐of‐plane directions including their relative degrees.

3D Printing Auxetic Architectures for Hypertrophic Scar Therapy

AbstractFitting the human body for different purposes such as flexible electronics and functional garments can be a challenging task. Pressure garments are used to treat hypertrophic scars (HSs)pr. However, they have often failed to provide consistent pressure during joint movement. To increase the therapy efficacy, the application is proposed of 3D printed thermoplastic polyurethane (TPU) with an auxetic architecture insert for pressure therapy. Auxetic material can undergo an out‐of‐plane bending into a synclastic curvature, which can easily accommodate the contours of the human body. In this study, the synclastic effect of the auxetic structure under out‐of‐plane bending is illustrated through finite element analysis (FEA) first. Next, the formability, structural deformation, and auxetic response of re‐entrant (RE) and double‐arrowhead (DAH) auxetic structures when loading by a spherical surface in out‐of‐plane direction are unprecedentedly evaluated experimentally and numerically. It can be observed the internal angle of auxetic structure plays an important role regarding shape formability. Nevertheless, the result of wear trial reveals this design facilitates a stable level of pressure during the body motion which promotes the recovery of HS. It is believed the characterized result of auxetic architectures not only contribute to HS therapy, but also any type of biomedical devices.

In-Plane Deformation Behavior and the Open Area of Rotating Squares in an Auxetic Compound Fabric.

A conventional compound fabric was used to develop a modern, multifunctional material with an auxetic behaviour and a tailored open area for particle filtration. Such material was produced using traditional textile technology and laser cutting, to induce a rotating squares unit geometry. The behaviour was investigated of three different rotating unit cell sizes. The laser slit thickness and the length of the hinges were equal for all three-unit cells. The tensile properties, Poisson’s ratio and auxetic behaviour of the tested samples were investigated, especially the influence of longitudinal displacement on the fabric’s open area and the filtered particle sizes (average and maximum). Results show that the developed compound fabric possesses an average negative Poisson’s ratio of up to −1, depending on the applied auxetic geometry. The larger rotating cell size samples offer a higher average negative Poisson’s ratio and a higher breaking strength due to the induced slits. The findings highlight the usefulness of patterned cuts in conventional textile materials to develop advanced auxetic textile materials with tailored geometrical and mechanical properties.

Onset of criticality in hyper-auxetic polymer networks

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson’s ratio ν. The amount of deformation in response to the applied force can be at most equal to the imposed one, so that ν = − 1 is the lowest bound for the mechanical stability of solids, a condition here defined as “hyper-auxeticity”. In this work, we numerically show that ultra-low-crosslinked polymer networks under tension display hyper-auxetic behavior at a finite crosslinker concentration. At this point, the nearby mechanical instability triggers the onset of a critical-like transition between two states of different densities. This phenomenon displays similar features as well as important differences with respect to gas-liquid phase separation. Since our model is able to faithfully describe real-world hydrogels, the present results can be readily tested in laboratory experiments, paving the way to explore this unconventional phase behavior.