Review on auxetic materials

Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, for almost all common materials the Poisson's ratio is positive. In 1987, Lakes first discovered negative Poisson's ratio effect in polyurethane (PU) foam with re-entrant structures, which was named anti-rubber, auxetic, and dilatational by later researchers. In this paper, the term 'auxetic' will be used. Since then, investigation on the auxetic materials has held major interest, focusing on finding more materials with negative Poisson's ratio, and on examining the mechanisms, properties and applications. Therefore, more materials were found to have the counter-intuitive effect of auxeticity due to different structural or microstructrual mechanisms. The present article reviews the latest advances in auxetic materials, their structural mechanisms, performance and applications.     

Fabrication methods for auxetic foams

Auxetic materials have a negative Poisson's ratio, that is, they expand laterally when stretched longitudinally. Negative Poisson's ratio is an unusual property that affects many of the mechanical properties of the material, such as indentation resistance, compression, shear stiffness, and certain aspects of the dynamic performance. The unusual mechanical properties of auxetic foams are attributed to the deformation characteristics of re-entrant microstructures. One way of obtaining negative Poisson's ratio is by using a re-entrant cell structure. Auxetic foam was fabricated from a conventional polymeric foam. The fabrication method for making both small and large auxetic foam specimens is described. This revised version was published online in November 2006 with corrections to the Cover Date.     

Auxetic materials: the positive side of being negative

An auxetic material is one which gets fatter when it is stretched. Thus, unlike most materials, it has a negative Poisson's ratio. This review looks at examples of auxetic materials, the effect the negative Poisson's ratio has on their mechanical properties and how these fascinating new materials can be used in applications as diverse as smart fasteners, replacement blood vessels and curved car door panels. It also considers the benefits of introducing such novel effects in undergraduate teaching     

Poisson's ratios of auxetic and other technological materials

Poisson's ratio, the relation between lateral contraction of a thin, linearly elastic rod when subjected to a longitudinal extension, has a long and interesting history. For isotropic bodies, it can theoretically range from +1/2 to -1; the experimental gamut for anisotropics is even larger. The ratio is positive for all combinations of directions in most crystals. But as far back as the 1800s, Voigt and others found that negative values were encountered for some materials, a property now called auxeticity. Here we examine this property from the point of view of crystal stability and compute extrema of the ratio for various interesting and technologically important materials. Potential applications of the auxetic property are mentioned.     

Microstructural modelling of auxetic microporous polymers

A simple two-dimensional model for the deformation of auxetic microporous polymers (those with a negative Poisson's ratio) has been developed. This model network of rectangular nodules interconnected by fibrils has been further developed to include the possibilities of fibril hinging, flexure and stretching. Expressions for strain-dependent Poisson's ratio and Young's modulus have been derived and compared with experimental results on microporous PTFE and UHMWPE. A combination of the hinging mode followed by the stretching mode of deformation can be used to explain the general features of the experimental data for these auxetic polymers. The force coefficients governing the different modes of deformation are dependent on fibril dimensions and intrinsic material properties. By varying the geometry of the network, the model can be used to predict different combinations of Poisson's ratio with modulus, from large positive through to large negative values.     

Analytical solution and finite element approach to the 3D re-entrant structures of auxetic materials

One of the methods in understanding the real microstructure of auxetic material is by separating it into several simplified structures that have distinct mechanisms. Among those simplified structures are chiral and re-entrant structures. This paper adapts a 2D re-entrant structure for a 3D auxetic structure. A re-entrant structure is chosen due to its fundamental characteristics underlying the main characteristics of auxetic materials. The energy methods of solid mechanics along with numerical methods are used to study the fundamental concept of auxetic materials. Understanding the characteristics of the re-entrant structure will lead to the better comprehension of other structures of auxetic materials, which will eventually contribute to the advance of research in this new class of materials.     

Deformation mechanisms in negative Poisson's ratio materials: structural aspects

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with noncentral force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.     

Development of novel auxetic structures based on braided composites

Auxetic materials are a class of materials that expand transversely when stretched longitudinally. Recently, auxetic materials are gaining special interest in the technical sectors mainly due to their attractive mechanical behavior. This paper reports, for the first time, the development of auxetic structures from composite materials and the characterization of their auxetic as well as mechanical properties. Five different auxetic structures were developed varying their structural angle using core reinforced braided composite rods, containing glass fibers for axial reinforcement, polyester filaments for braided structure and epoxy resin as the matrix. Auxetic behavior of these structures was studied in a tensile testing machine using an image-based tracking method. Additionally, an analytical model was used to calculate Poisson’s ratio of these structures. According to experimental and analytical results, auxetic behavior and tensile characteristics of these structures were strongly dependant on their initial geometric configuration (i.e. structural angle). These novel auxetic structures exhibited Poisson’s ratio in the range of −0.30 to −5.20.     

Composites with auxetic inclusions showing both an auxetic behavior and enhancement of their mechanical properties

Composite materials made of auxetic inclusions and giving rise overall to negative Poisson’s ratio are considered, adopting a two-steps micromechanical approach for the calculation of their effective mechanical properties. The inclusions consist of periodic beam lattices, whose equivalent mechanical properties are calculated by a discrete homogenization scheme in a first step. The hexachiral and hexagonal reentrant lattices are considered as representative of the two main deformation mechanisms responsible for auxeticity. In a second step, the equivalent properties of the composite are calculated from numerical homogenization using the finite element method. It is shown that both an auxetic behavior and enhanced moduli can be obtained for not too slender micro-beams.     

A generalised three-dimensional tethered-nodule model for auxetic materials

Models for the nano/micro-structural deformation and mechanical properties of auxetic materials (i.e. materials with a negative Poisson’s ratio) have been previously developed. However, most of these models have been two-dimensional, were usually designed specifically to describe some particular class of auxetic materials, and generally only described the behaviour of one particular plane whilst completely ignoring the out-of-plane behaviour of the material. A three-dimensional model has been developed which can be applied to several classes of auxetic materials, including microporous expanded polymers such as e-PTFE, e-UHMWPE and e-PA, body-centered cubic metals and foams. It is generalised that its underlying structure is not specific to a lengthscale or material as the previous list shows. The new model offers a better insight into the underlying principles behind the observed auxetic behaviour and offers a significant improvement in the agreement of the models with existing experimental data. It is shown that there are geometric limitations to the number of planes that can simultanesously display auxetic behaviour. This has ramifications on the design of ordered auxetic materials.     

Development,characterization and analysis of auxetic structures from braided composites and study the influence of material and structural parameters

Auxetic materials are gaining special interest in technical sectors due to their attractive mechanical behaviour. This paper reports a systematic investigation on missing rib design based auxetic structures produced from braided composites for civil engineering applications. The influence of various structural and material parameters on auxetic and mechanical properties was thoroughly investigated. The basic structures were also modified with straight longitudinal rods to enhance their strengthening potential in structural elements. Additionally, a new analytical model was proposed to predict Poisson’s ratio through a semi empirical approach. Auxetic and tensile behaviours were also predicted using finite element analysis. The auxetic and tensile behaviours were observed to be more strongly dependent on their structural parameters than the material parameters. The developed analytical models could well predict the auxetic behaviour of these structures except at very low or high strains. Good agreement was also observed between the experimental results and numerical analysis.     

负泊松比微结构拓扑优化设计

在构建负泊松比结构拓扑优化模型时,直接用负泊松比的数学表达式构造目标函数,将使得目标函数高度非线性,迭代过程敏度分析困难。采用线性拟合法,构建了具有线性特征的负泊松比微结构拓扑优化目标函数,基于能量法和均匀化方法,结合拓扑优化理论,构建了一种可以快速准确求解负泊松比的拓扑优化设计模型,求解该模型得到了一种优化的拓扑构型及相应的负泊松比值。根据优化求解得到的结构模型,参考国家标准GB/T 22315-2008《金属材料弹性模量和泊松比试验方法》,利用有限元软件对其泊松比进行仿真计算,然后采用激光加工方式制造试样,并测试其泊松比,经过与优化模型求解得到的泊松比值对比分析,验证了所构建优化模型的正确性。本文方法既避免了以负泊松比表达式为优化函数时会出现的高度非线性问题,也降低了求解的复杂程度,为负泊松比微结构的设计提供了一种参考方法。     

Microscopic examination of the microstructure and deformation of conventional and auxetic foams

Auxetic materials have a negative Poisson’s ratio, that is, they expand laterally when stretched longitudinally. One way of obtaining a negative Poisson’s ratio is by using a re-entrant cell structure. Auxetic foam was fabricated from a conventional polymeric foam. Assuming similar mechanical properties for the solid material comprising the foams, the principle variable affecting the properties of the foam is the geometry of the cells. This means that the unusual mechanical properties of auxetic foams are attributed to the deformation characteristics of re-entrant microstructures. In this paper, the results of optical- and scanning electron-microscopic studies of the geometrical parameters for the different foams examined are presented. Examples of the microstructural deformation mechanisms observed are also presented. Comparison between the conventional foams and their auxetic conversions are also made. This revised version was published online in November 2006 with corrections to the Cover Date.     

The strain dependent indentation resilience of auxetic microporous polyethylene

A series of tests have been conducted on (i) auxetic, (ii) compression moulded and (iii) sintered ultra high molecular weight polyethylene. The auxetic material possesses a negative Poisson's ratio, , due to its complex porous microstructure which consists of nodules interconnected by fibrils and the sintered material has a positive and is microporous but does not contain fibrils. It was found that the auxetic material was both more difficult to indent than the other materials at low loads (from 10–100 N) and was the least plastic with the most rapid viscoelastic creep recovery of any residual deformation. Indeed, at low loads, where the resistance to local indentation is most elastic, the hardness increased by up to a factor of 8 on changing the Poisson's ratio from 0 to –0.8. A mechanism is proposed based on local densification under the indentor of the nodules and fibrils which explains how the microstructural response of an auxetic polymer can be used to interpret the results.     

The manufacture and characterisation of a novel,low modulus,negative Poisson’s ratio composite

Relatively few negative Poisson’s ratio (auxetic) composites have been manufactured and characterised and none with inherently auxetic phases [Milton G. J. Mech. Phys. Solids 1992;40:1105–37]. This paper presents the use of a novel double-helix yarn that is shown to be auxetic, and an auxetic composite made from this yarn in a woven textile structure. This is the first reported composite to exhibit auxetic behaviour using inherently auxetic yarns. Importantly, both the yarn and the composite are produced using standard manufacturing techniques and are therefore potentially useful in a wide range of engineering applications.     

Stress Intensity Factor and Plastic Zone of Auxetic Materials: A Fracture Mechanics Approach to a Chiral Structure Having Negative Poisson’s Ratio

This article summarizes the method of analytical formulation and computational approach of stress intensity factor and plastic zone calculation for auxetic materials, which have negative Poisson’s ratio. A chiral structure-based material is selected as an object of the study due to its popularity. The stress intensity factor is used in combination with the von Mises yielding condition to estimate the plastic zone’s shape and size. The results show that macroscopically the shape of the plastic zone for auxetic material is the same with that of ordinary materials. However, its size is smaller due to the reduction in its Young’s modulus from the solid material of which the auxetic material is made. Microscopically, an auxetic material has its plastic zone shape that is unique to its microstructure. Homogenization theory was convenient to use to bridge between the microscopic and macroscopic models.     

Thermal Stresses in Auxetic Plates and Shells

Solids that possess negative Poisson's ratio are termed auxetic materials. This article considers the effect of auxeticity, i.e., the negative extent of Poisson's ratio on thermal stresses in plates, shells, and other solids. Results show that in cases where temperature gradient is in the through-thickness of a fully-clamped plate or when the temperature gradient is in the radial direction of fully-clamped shells, the thermal stresses can be significantly reduced by using auxetic materials. The same result applies to spheres and cylinders with radial temperature gradient. The maximum thermal stress is minimized if the selected material possesses Poisson's ratio of –1. However, the use of auxetic material is not always advantageous, nor does the use of materials with Poisson's ratio of –1 always minimize the maximum thermal stresses. It is herein suggested that, in addition to the use of materials with lower modulus and lower coefficient of thermal expansion, the use of auxetic materials offers an alternative route for lowering thermal stresses in some cases.     

负泊松比三明治结构填充泡沫混凝土的面内压缩性能

为改善负泊松比三明治结构的受压破坏模式且提高其缓冲吸能能力,提出一种填充泡沫混凝土的新型复合三明治结构。在负泊松比结构中填充不同密度(409 kg/m3、575 kg/m3、848 kg/m3、1 014 kg/m3)的泡沫混凝土得到负泊松比填充结构,并对无填充负泊松比结构、负泊松比填充结构和泡沫混凝土对照试块在准静态压缩下的破坏模式和吸能特性进行比较。根据荷载-位移关系和破坏模式得到以下结论:当填充物密度较小时,负泊松比填充结构能够将填充物的泊松比限制在较小的数值,胞元表现出内凹的变形模式,结构发生逐渐被压实的压缩破坏;当填充物密度较大时,结构发生“X”型剪切破坏,塑性铰区域和剪切带附近的胞壁发生断裂破坏;泡沫混凝土填充物的密度越大,填充结构的压实应变越小,吸收的能量越多,但当填充物密度超过一定值后,填充物密度的增加对负泊松比填充结构能量吸收能力的提升作用不再明显,结构的比吸能降低。      

Prediction of structures and mechanical properties of composites using a genetic algorithm and finite element method

A combined method of a genetic algorithm and finite element stress analysis has been developed to design the structure of materials. The genetic algorithm is applied to searching structures that have a desired property by combining it with the finite element analysis, which is used to predict the elastic modulus and Poisson's ratio. The calculation of the stress analysis is validated from the comparison with the theory on parallel, series, and random structures. The combined method was applied to two searches of structures. One was to find structures that have a desired elastic modulus, respectively. The calculation successfully found a proper structure for each desired elastic modulus. The other was the search of the structure that shows a negative Poisson's ratio. A structure having the negative Poisson's ratio was generated by the calculation. Although this original structure would appear to have no features, it gave us a good idea for the design of materials by investigating the stress distribution in the original structure. A new structure that consists of a unique and continuous pattern of the higher elastic component was designed from the calculation. The reason for the negative Poisson's ratio is explained by mechanical linkage.     

Experimental and numerical determination of the lubrication force between a spherical particle and a micro-structured surface

In many particulate processes suspensions need to be handled. Hydrodynamic forces in presence of a liquid as a surrounding continuum medium can significantly affect the particle collision behaviour. When particles approach a wall, lubrication force can become dominant with decreasing distance. This force was described analytically by different authors for a smooth flat wall. Roughness was found to be an important factor in this context, but the mechanisms are still not fully understood. In this work, the effects of topology on the lubrication force were studied using a regular prismatic micro-structured titanium surface produced by micro-milling. A nanoindentation setup was modified for the direct measurement of this force during the particle approach to polished and micro-structured surfaces in liquid. For a more detailed insight on the behaviour of the fluid in the decreasing gap between particle and surface microstructure, resolved computational fluid dynamics (CFD) simulations were performed using an overset mesh method. The comparison of simulation results with nanoindentation tests and analytical solution showed a good agreement. The effects of structure size and particle contact location at various approaching velocities on the lubrication force were investigated.