Review of Auxetic Materials for Sports Applications: Expanding Options in Comfort and Protection

A robust, high-temperature-resistant, protective cellulose gel enabled by multiscale structural engineering

Given the escalating environmental and safety concerns, friendly protective materials with exceptional mechanical properties, biodegradability, and insensitivity to high temperature have received more and more attention. Here, we report a robust cellulosic gel through the multi-scale integration of cellulose molecular skeleton, nano-reinforced diatomite, and in situ polymerized polyacrylamide molecule. The bottom-up yet cross-scale approach facilitates the formation of cellulosic gel characterized by a highly interconnected hydrogen bond network and nano-enhanced domain, resulting in a tensile strength of up to 13.83 MPa, a Young's modulus exceeding 280 MPa, and an impact strength around 12.38 KJ m-1. Furthermore, this gel exhibits structural stability at temperatures up to 130 °C, good flame retardancy, and complete biodegradability within a span of 35 days. The robust cellulosic gel, acting as a pliable protector, demonstrates exceptional protection for human joints. Our study presents a highly efficient and scalable pathway towards the development of sustainable and robust biomass gels, holding immense potential in intelligent-protective wearables and advanced materials science and engineering.

Efficacy of auxetic lattice structured shoe sole in advancing footwear comfort-From the perspective of plantar pressure and contact area

Introduction

Designing footwear for comfort is vital for preventing foot injuries and promoting foot health. This study explores the impact of auxetic structured shoe soles on plantar biomechanics and comfort, motivated by the integration of 3D printing in footwear production and the superior mechanical properties of auxetic designs. The shoe sole designs proposed in this study are based on a three-dimensional re-entrant auxetic lattice structure, orthogonally composed of re-entrant hexagonal honeycombs with internal angles less than 90 degrees. Materials fabricated using this lattice structure exhibit the characteristic of a negative Poisson's ratio, displaying lateral expansion under tension and densification under compression.

Methods

The study conducted a comparative experiment among three different lattice structured (auxetic 60°, auxetic 75° and non-auxetic 90°) thermoplastic polyurethane (TPU) shoe soles and conventional polyurethane (PU) shoe sole through pedobarographic measurements and comfort rating under walking and running conditions. The study obtained peak plantar pressures (PPPs) and contact area across seven plantar regions of each shoe sole and analyzed the correlation between these biomechanical parameters and subjective comfort.

Results

Compared to non-auxetic shoe soles, auxetic structured shoe soles reduced PPPs across various foot regions and increased contact area. The Auxetic 60°, which had the highest comfort ratings, significantly lowered peak pressures and increased contact area compared to PU shoe sole. Correlation analysis showed that peak pressures in specific foot regions (hallux, second metatarsal head, and hindfoot when walking; second metatarsal head, third to fifth metatarsal head, midfoot, and hindfoot when running) were related to comfort. Furthermore, the contact area in all foot regions was significantly associated with comfort, regardless of the motion states.

Conclusion

The pressure-relief performance and conformability of the auxetic lattice structure in the shoe sole contribute to enhancing footwear comfort. The insights provided guide designers in developing footwear focused on foot health and comfort using auxetic structures.

Characterization of Exterior Parts for 3D-Printed Humanoid Robot Arm with Various Patterns and Thicknesses

Currently, metal is the most common exterior material used in robot development due to the need to protect the motor. However, as soft, wearable, and humanoid robots are gradually being developed, many robot parts need to be converted into artificial skin using flexible materials. In this study, in order to develop soft exterior parts for robots, we intended to manufacture exterior robot arm parts via fused filament fabrication (FFF) 3D printing according to various structural and thickness conditions and analyze their mechanical properties. The exterior parts of the robot arms were manufactured utilizing Shore 95 A TPU (eTPU, Esun, Shenzhen, China), which is renowned for its softness and exceptional shock absorption characteristics. The exterior robot arm parts were modeled in two parts, the forearm and upper arm, by applying solid (SL) and re-entrant (RE) structures and thicknesses of 1, 2, and 4 mm. The mechanical properties were analyzed through the use of three-point bending, tensile, and compression testing. All of the characterizations were analyzed using a universal testing machine (AGS-X, SHIMADZU, Kyoto, Japan). After testing the samples, it was confirmed that the RE structure was easily bendable towards the bending curve and required less stress. In terms of the tensile tests, the results were similar to the bending tests; to achieve the maximum point, less stress was required, and for the compression tests, the RE structure was able to withstand the load compared to the SL structure. Therefore, after analyzing all three thicknesses, it was confirmed that the RE structure with a 2 mm thickness had excellent characteristics in terms of bending, tensile, and compressive properties. Therefore, the re-entrant pattern with a 2 mm thickness is more suitable for manufacturing a 3D-printed humanoid robot arm.

Adaptive plasticity of auxetic Kirigami hydrogel fabricated from anisotropic swelling of cellulose nanofiber film

Hydrogels are flexible materials that typically accommodate elongation with positive Poisson's ratios. Auxetic property, i.e., the negative Poisson's ratio, of elastic materials can be macroscopically implemented by the structural design of the continuum. We realize it without mold for hydrogel made of cellulose nanofibers (CNFs). The complex structural design of auxetic Kirigami is first implemented on the dry CNF film, i.e., so-called nanopaper, by laser processing, and the CNF hydrogel is formed by dipping the film in liquid water. The CNF films show anisotropic swelling where drastic volumetric change mainly originates from increase in the thickness. This anisotropy makes the design and fabrication of the emergent Kirigami hydrogel straightforward. We characterize the flexibility of this mechanical metamaterial made of hydrogel by cyclic tensile loading starting from the initial end-to-end distance of dry sample. The tensile load at the maximum strain decreases with the increasing number of cycles. Furthermore, the necessary work up to the maximum strain even decreases to the negative value, while the work of restoration to the original end-to-end distance increases from the negative value to the positive. The equilibrium strain where the force changes the sign increases to reach a plateau. This plastic deformation due to the cyclic loading can be regarded as the adaptive response without fracture to the applied dynamic loading input.

Mathematical simulation of damage detection for fighting athletes and equipment based on conjugated polymer development

Traditional combat sports equipment usually uses synthetic materials, such as polyurethane and synthetic leather. Although these materials have a certain degree of strength and durability, they have poor flexibility and antibacterial properties, making it difficult to provide stable support and protection for athletes. In order to enhance the antibacterial properties and flexibility of sports equipment and reduce the risk of injuries to athletes, this article conducts in-depth research on the development of combat sports equipment using conjugated polymers. This article first selects polypropylene (PP) as the base material for sports equipment for combat athletes, and uses the gas phase polymerization method to prepare the material; then uses chitosan as an antimicrobial agent and uses the oxidative degradation method to prepare it; after that, this article coats the chitosan antibacterial agent on the prepared PP material, and uses a combination of dipping and calendering for antibacterial treatment; finally, this article uses the spunbond melt-blown composite method to fill and combine the top equipment of combat athletes to achieve the structural design of sports equipment. In order to verify the effectiveness of the equipment, this article conducted equipment performance testing and sports injury simulation. The results showed that the average diameter of the antibacterial zone of this sports equipment reached more than 1 mm, and in the injury risk test, the risk of athletes' joint and muscle injuries was reduced by 16.9% and 20.5% respectively. Research shows that developing combat sports equipment based on conjugated polymers can help reduce the risk of injury to athletes and improve the safety of combat sports.

An examination of auxetic componentry for applications in human-centred biomedical product design settings

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.

Auxetic polymer networks: The role of crosslinking, density, and disorder

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels.

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.

Auxetic Behaviour of Rigid Connected Squares

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.

Development, fabrication and mechanical characterisation of auxetic bicycle handlebar grip

The auxetic cellular structures are one of the most promising metamaterials for vibration damping and crash absorption applications. Therefore, their use in the bicycle handlebar grip was studied in this work. A preliminary computational design study was performed using various auxetic and non-auxetic geometries under four load cases, which can typically appear. The most representative geometries were then selected and fabricated using additive manufacturing. These geometries were then experimentally tested to validate the discrete and homogenised computational models. The homogenised computational model was then used to analyse the biomechanical behaviour of the handlebar grip. It was observed that handle grip made from auxetic cellular metamaterials reduce the high contact pressures, provide similar stability and hereby improve the handlebar ergonomics.

Micro-Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of micro-scale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.

Metamaterial with Tunable Positive and Negative Hygrothermal Expansion Inspired by a Four-Fold Symmetrical Islamic Motif

A metamaterial with controllable positive and negative thermal and hygroscopic expansions is investigated herein by inspiration from a range of Islamic geometric patterns. Constructing from eight pairs of pin-jointed Y-elements, each unit cell manifests eight rhombi that are arranged circumferentially, thereby manifesting four axes of symmetry. By attachment of bimaterial spiral springs of contrasting expansion coefficients to the far arms of the paired Y-elements, a change in the environment’s thermal or hygroscopic condition alters the offset angle of the paired Y-elements such that the unit cell of the metamaterial ranges from the eight-pointed star to the regular octagon. The effective coefficient of thermal expansion (CTE) and the coefficient of moisture expansion (CME) of this metamaterial were developed for small and large changes in environmental fluctuations using infinitesimal and finite models, respectively. Generated data indicates that the sign and magnitude of the effective thermal and hygroscopic expansion coefficients can be controlled by geometrical descriptors of the bimaterial spiral spring—such as its coil number and the ratio of its mean radius to its thickness—as well as the properties of the bimaterial’s layers such as their expansion coefficients, Young’s moduli and, in the case of effective hygroscopic expansion, their relative absorptivity. The obtained results suggest that the proposed metamaterial can be designed to perform as highly sensitive thermal and/or moisture sensors, as well as other functional materials or devices that take advantage of environmental changes as stimuli.

Enabling Durable Ultralow-k Capacitors with Enhanced Breakdown Strength in Density-Variant Nanolattices

Ultralow-k materials used in high voltage devices require mechanical resilience and electrical and dielectric stability even when subjected to mechanical loads. Existing devices with organic polymers suffer from low thermal and mechanical stability while those with inorganic porous structures struggle with poor mechanical integrity. Recently, 3D hollow-beam nanolattices have emerged as promising candidates that satisfy these requirements. However, their properties are maintained for only five stress cycles at strains below 25%. Here, we demonstrate that alumina nanolattices with different relative density distributions across their height elicit a deterministic mechanical response concomitant with a 1.5-3.3 times higher electrical breakdown strength than nanolattices with uniform density. These density-variant nanolattices exhibit an ultralow-k of ≈1.2, accompanied by complete electric and dielectric stability and mechanical recoverability over 100 cyclic compressions to 62.5% strain. We explain the enhanced insulation and long-term cyclical stability by the bi-phase deformation where the lower-density region protects the higher-density region as it is compressed before the higher-density region, allowing to simultaneously possess high strength and ductility like composites. This study highlights the superior electrical performance of the bi-phase nanolattice with a single interface in providing stable conduction and maximum breakdown strength.

Study on the Tensile Behavior of Helical Auxetic Yarns with Finite Element Method

Complex yarns with helical wrapping structure show auxetic effect under axial tension and a wide perspective application. Experimental results suggested that initial helical angle was one of the most important structural parameters. However, the experimental method was limited and could not effectively explain the deformation behavior or auxetic mechanism. A finite element model of the helical auxetic yarn was built and used to analyze the interactive relationship between the two components and the stress distribution mode. The effectiveness and accuracy of the model was first verified by comparing with the experimental results. The simulation results showed that the complex yarn with initial helical angle of 14.5° presented the maximum negative Poisson's ratio of -2.5 under 5.0% axial strain. Both the contact property between the two components and the radial deformability of the elastic core filament were key factors of the auxetic property. When the contact surfaces were completely smooth and the friction coefficient μ was set to 0, the complex yarn presented non-auxetic behavior. When the Poisson's ratio of the core filament was 0, the complex yarn showed greater auxetic effect. During the axial stretching, the tensile stress was mainly distributed in the wrap filament, which led to structural deformation and auxetic behavior. A pair of auxetic yarns showed pore effect and high expansion under axial strain. Thus, it may be necessary to consider new weaving structures and preparation methods to obtain the desired auxetic property and application of auxetic yarns.

Numerical Analysis of Dynamic Properties of an Auxetic Structure with Rotating Squares with Holes

In this paper, a novel auxetic structure with rotating squares with holes is investigated. The unit cell of the structure consists of four units in the shape of a square with cut corners and holes. Finally, the structure represents a kind of modified auxetic structure made of rotating squares with holes or sheets of material with regularly arranged diamond and square cuts. Effective and dynamic properties of these structures depend on geometrical properties of the structure. The structures are characterized by an effective Poisson's ratio from negative to positive values (from about minus one to about plus one). Numerical analysis is made for different geometrical features of the unit cells. The simulations enabled the determination of the dynamic characteristic of the analyzed structures using vibration transmission loss, transmissibility, and mechanical impedance. Numerical calculations were conducted using the finite element method. In the analyzed cases of cellular auxetic structures, a linear elasticity model of the material is assumed. The dynamic characteristic of modified rotating square structures is strongly dependent not only on frequency. The dynamic behavior could also be enhanced by adjusting the geometric parameter of the structure. Auxetic and non-auxetic structures show different static and dynamic properties. The dynamic properties of the analyzed structures were examined in order to determine the frequency ranges of dynamic loads for which the values of mechanical impedance and transmissibility are appropriate.

Computational Study of Non-Porous Auxetic Plates with Diamond Shape Inclusions

Creating non-porous structures that offer auxetic behavior can have a variety of industrial applications, especially when the porosity impairs the functionality of the auxetic structures. This study presents the design and finite element analysis of architected bi-material auxetic plates consisting of repeating unit cells that comprise rigid rotary units and soft inclusions. The change in the design parameters of unit cells produces a variety of mechanical properties, such as different levels of Poisson’s ratio and stiffness for the architected plates that can result in specific static or dynamic responses. The natural frequencies and deflection under uniform lateral loading of the architected plates with clamped boundary conditions were investigated. Furthermore, the effectiveness of the homogenization technique based on the mechanical properties obtained from finite element analysis in predicting the dynamic and static response of the architected plate was also studied.

Low-Velocity Impact Response of Auxetic Seamless Knits Combined with Non-Newtonian Fluids

Low-velocity impact can cause serious damage to the person or structure that is hit. The development of barriers that can absorb the energy of the impact and, therefore, protect the other side of the impact is the ideal solution for the pointed situation. Auxetic materials and shear thickening fluids are two types of technologies that have great capabilities to absorb high levels of energy when an impact happens. Accordingly, within this study, the combination of auxetic knits with shear thickening fluids by the pad-dry-cure process was investigated. It was observed that, by applying knits with auxetic patterns produced with denser materials and combined with the shear thickening fluids, high performance in terms of absorbed energy from puncture impact is obtained. The increment rates obtained are higher than 100% when comparing the structures with and without shear thickening fluids.

Auxetic Metamaterials for Biomedical Devices: Current Situation, Main Challenges, and Research Trends

Auxetic metamaterials are characterized by a negative Poisson ratio (NPR) and display an unexpected property of lateral expansion when stretched and densification when compressed. Auxetic properties can be achieved by designing special microstructures, hence their classification as metamaterials, and can be manufactured with varied raw materials and methods. Since work in this field began, auxetics have been considered for different biomedical applications, as some biological tissues have auxetic-like behaviour due to their lightweight structure and morphing properties, which makes auxetics ideal for interacting with the human body. This research study is developed with the aim of presenting an updated overview of auxetic metamaterials for biomedical devices. It stands out for providing a comprehensive view of medical applications for auxetics, including a focus on prosthetics, orthotics, ergonomic appliances, performance enhancement devices, in vitro medical devices for interacting with cells, and advanced medicinal clinical products, especially tissue engineering scaffolds with living cells. Innovative design and simulation approaches for the engineering of auxetic-based products are covered, and the relevant manufacturing technologies for prototyping and producing auxetics are analysed, taking into consideration those capable of processing biomaterials and enabling multi-scale and multi-material auxetics. An engineering design rational for auxetics-based medical devices is presented with integrative purposes. Finally, key research, development and expected technological breakthroughs are discussed.

Curvature Induced by Deflection in Thick Meta-Plates

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs

Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller.

On the application of additive manufacturing methods for auxetic structures: a review

Auxetic structures are a special class of structural components that exhibit a negative Poisson's ratio (NPR) because of their constituent materials, internal microstructure, or structural geometry. To realize such structures, specialized manufacturing processes are required to achieve a dimensional accuracy, reduction of material wastage, and a quicker fabrication. Hence, additive manufacturing (AM) techniques play a pivotal role in this context. AM is a layer-wise manufacturing process and builds the structure as per the designed geometry with appreciable precision and accuracy. Hence, it is extremely beneficial to fabricate auxetic structures using AM, which is otherwise a tedious and expensive task. In this study, a detailed discussion of the various AM techniques used in the fabrication of auxetic structures is presented. The advancements and advantages put forward by the AM domain have offered a plethora of opportunities for the fabrication and development of unconventional structures. Therefore, the authors have attempted to provide a meaningful encapsulation and a detailed discussion of the most recent of such advancements pertaining to auxetic structures. The article opens with a brief history of the growth of auxetic materials and later auxetic structures. Subsequently, discussions centering on the different AM techniques employed for the realization of auxetic structures are conducted. The basic principle, advantages, and disadvantages of these processes are discussed to provide an in-depth understanding of the current level of research. Furthermore, the performance of some of the prominent auxetic structures realized through these methods is discussed to compare their benefits and shortcomings. In addition, the influences of geometric and process parameters on such structures are evaluated through a comprehensive review to assess their feasibility for the later-mentioned applications. Finally, valuable insights into the applications, limitations, and prospects of AM for auxetic structures are provided to enable the readers to gauge the vitality of such manufacturing as a production method.

Study on a Chiral Structure with Tunable Poisson's Ratio

A chiral structure with a negative Poisson's ratio containing a hollow circle with varying diameters was designed, and the finite element method was used to investigate the variation in the Poisson's ratio when the hollow circle diameter was varied (d = 0, 1, 2, 3, and 4 mm). The simulation results showed that the Poisson's ratio was sensitive to the hollow circle diameter, and the minimum Poisson's ratio was -0.43. Three specimens with different hollow circle diameters (d' = 0, 1, and 3 mm) were 3D-printed from thermoplastic polyurethane, and the Poisson's ratio and equivalent elastic modulus were measured. In the elastic range, the Poisson's ratio increased and the equivalent elastic modulus decreased as the hollow circle diameter increased. The simulation and experimental results showed good agreement. The proposed structure is expected to be applicable to protective sports gear owing to its high energy absorption and the fact that its properties can be modified as required by adjusting the geometric parameters of the unit cell.

An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns

A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of −1, is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of the Ghiyathiyya Madrasa in Khargird, Iran (built 1438–1444 AD). Each unit of the metamaterial consists of eight pairs of pin-jointed Y-shaped rigid elements, whereby every pair of Y-elements is elastically restrained by a spiral spring. Upon intermediate stretching, each metamaterial unit resembles the north dome of Jameh Mosque, Iran (built 1087–1088 AD), until the attainment of the fully opened configuration, which resembles a structure in Agra, India, near the Taj Mahal. Both infinitesimal and finite deformation models of the effective Young’s modulus for the metamaterial structure were established using strain energy approach in terms of the spiral spring stiffness and geometrical parameters, with assumptions to preserve the eight-fold symmetricity of every metamaterial unit. Results indicate that the prescription of strain raises the effective Young’s modulus in an exponential manner until full extension is attained. This metamaterial is useful for applications where the overall shape of the structure must be conserved in spite of uniaxial application of load, and where deformation is permitted under limited range, which is quickly arrested as the deformation progresses.

Effect of Compressive Strain Rate on Auxetic Foam

Auxetic foams have previously been shown to have benefits including higher indentation resistance than their conventional counterparts, due to their negative Poisson’s ratio, making them better at resisting penetration by concentrated loads. The Poisson’s ratio and Young’s modulus of auxetic open cell foams have rarely been measured at the high compressive strain rates typical during impacts of energy absorbing material in sporting protective equipment. Auxetic closed cell foams are less common than their open cell counterparts, and only their quasi-static characteristics have been previously reported. It is, therefore, unclear how the Poisson’s ratio of auxetic foam, and associated benefits such as increased indentation resistance shown at low strain rates, would transfer to the high strain rates expected under impact. The aim of this study was to measure the effect of strain rate on the stiffness and Poisson’s ratio of auxetic and conventional foam. Auxetic open cell and closed cell polymer foams were fabricated, then compression tested to ~80% strain at applied rates up to 200 s−1, with Poisson’s ratios obtained from optical full-field strain mapping. Open cell foam quasi-static Poisson’s ratios ranged from −2.0 to 0.4, with a narrower range of −0.1 to 0.3 for closed cell foam. Poisson’s ratios of auxetic foams approximately halved in magnitude between the minimum and maximum strain rates. Open cell foam quasi-static Young’s moduli were between 0.02 and 0.09 MPa, whereas closed cell foams Young’s moduli were ~1 MPa, which is like foam in protective equipment. The Young’s moduli of the auxetic foams approximately doubled at the highest applied strain rate of 200 s−1.

Numerical Investigation of Auxetic Textured Soft Strain Gauge for Monitoring Animal Skin

Recent advances in hyperelastic materials and self-sensing sensor designs have enabled the creation of dense compliant sensor networks for the cost-effective monitoring of structures. The authors have proposed a sensing skin based on soft polymer composites by developing soft elastomeric capacitor (SEC) technology that transduces geometric variations into a measurable change in capacitance. A limitation of the technology is in its low gauge factor and lack of sensing directionality. In this paper, we propose a corrugated SEC through surface texture, which provides improvements in its performance by significantly decreasing its transverse Poisson's ratio, and thus improving its sensing directionality and gauge factor. We investigate patterns inspired by auxetic structures for enhanced unidirectional strain monitoring. Numerical models are constructed and validated to evaluate the performance of textured SECs, and to study their performance at monitoring strain on animal skin. Results show that the auxetic patterns can yield a significant increase in the overall gauge factor and decrease the stress experienced by the animal skin, with the re-entrant hexagonal honeycomb pattern outperforming all of the other patterns.

Liquid-Crystal-Elastomer-Based Dissipative Structures by Digital Light Processing 3D Printing

Digital Light Processing (DLP) 3D printing enables the creation of hierarchical complex structures with specific micro- and macroscopic architectures that are impossible to achieve through traditional manufacturing methods. Here, this hierarchy is extended to the mesoscopic length scale for optimized devices that dissipate mechanical energy. A photocurable, thus DLP-printable main-chain liquid crystal elastomer (LCE) resin is reported and used to print a variety of complex, high-resolution energy-dissipative devices. Using compressive mechanical testing, the stress-strain responses of 3D-printed LCE lattice structures are shown to have 12 times greater rate-dependence and up to 27 times greater strain-energy dissipation compared to those printed from a commercially available photocurable elastomer resin. The reported behaviors of these structures provide further insight into the much-overlooked energy-dissipation properties of LCEs and can inspire the development of high-energy-absorbing device applications.

Cellular Auxetic Structures for Mechanical Metamaterials: A Review

Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called "designed materials" or "architectured materials" and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson's ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.

DEFORMATION INDEX APPLIED TO IMPACT

Almost three decades ago, S. Futamura devised the deformation index concept for determining the control parameter for the viscoelastic response of deformed elastomers. We have extended this concept to impact mitigation, wherein material hardness and energy dissipation typically both affect the behavior. Laboratory impact tests were carried out on a series of compounds to deduce the deformation index pertinent to the rubber component. We then analyzed ballistic experiments, wherein material failure is associated with more complex conditions. The utility and limitations of this approach are discussed.

A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility

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

3D Device for Forces in Swimming Starts and Turns

Biomechanical tools capable of detecting external forces in swimming starts and turns have been developed since 1970. This study described the development and validation of a three-dimensional (six-degrees of freedom) instrumented block for swimming starts and turns. Seven force plates, a starting block, an underwater structure, one pair of handgrips and feet supports for starts were firstly designed, numerically simulated, manufactured and validated according to the Fédération Internationale de Natation rules. Static and dynamic force plate simulations revealed deformations between 290 to 376 µε and 279 to 545 µε in the anterior-posterior and vertical axis and 182 to 328.6 Hz resonance frequencies. Force plates were instrumented with 24 strain gauges each connected to full Wheatstone bridge circuits. Static and dynamic calibration revealed linearity ( R 2 between 0.97 and 0.99) and non-meaningful cross-talk between orthogonal (1%) axes. Laboratory and ecological validation revealed the similarity between force curve profiles. The need for discriminating each upper and lower limb force responses has implied a final nine-force plates solution with seven above and two underwater platforms. The instrumented block has given an unprecedented contribution to accurate external force measurements in swimming starts and turns.

High Partial Auxeticity Induced by Nanochannels in [111]-Direction in a Simple Model with Yukawa Interactions

Computer simulations using Monte Carlo method in the isobaric-isothermal ensemble were used to investigate the impact of nanoinclusions in the form of very narrow channels in the [ 111 ] -direction on elastic properties of crystals, whose particles interact via Yukawa potential. The studies were performed for several selected values of Debye screening length ( ( κ σ ) - 1 ). It has been observed that introduction of the nanoinclusions into the system reduces the negative value of Poisson's ratio towards [ 110 ] [ 1 1 ¯ 0 ] , maintaining practically constant values of Poisson's ratio in the directions [ 100 ] and [ 111 ] . These studies also show that concentration of particles forming the nanoinclusions in the system has a significant effect on the value of Poisson's ratio in the [ 110 ] [ 1 1 ¯ 0 ] -direction. A strong (more than fourfold) decrease of Poisson's ratio in this direction was observed, from - 0.147 ( 3 ) (system without inclusions) to - 0.614 ( 14 ) (system with nanoinclusions) at κ σ = 10 when the inclusion particles constituted about 10 percent of all particles. The research also showed an increase in the degree of auxeticity in the system with increasing concentration of nanoinclusion particles for all the screening lengths considered.

Mechanical Metamaterials Foams with Tunable Negative Poisson's Ratio for Enhanced Energy Absorption and Damage Resistance

Systematic and deep understanding of mechanical properties of the negative Poisson’s ratio convex-concave foams plays a very important role for their practical engineering applications. However, in the open literature, only a negative Poisson’s ratio effect of the metamaterials convex-concave foams is simply mentioned. In this paper, through the experimental and finite element methods, effects of geometrical morphology on elastic moduli, energy absorption, and damage properties of the convex-concave foams are systematically studied. Results show that negative Poisson’s ratio, energy absorption, and damage properties of the convex-concave foams could be tuned simultaneously through adjusting the chord height to span ratio of the sine-shaped cell edges. By the rational design of the negative Poisson’s ratio, when compared to the conventional open-cell foams of equal mass, convex-concave foams could have the combined advantages of relative high stiffness and strength, enhanced energy absorption and damage resistance. The research of this paper provides theoretical foundations for optimization design of the mechanical properties of the convex-concave foams and thus could facilitate their practical applications in the engineering fields.