Holographic study of conventional and negative Poisson's ratio metallic foams: elasticity,yield and micro-deformation

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modelling on the basis of cellular rib bending. The re-entrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.     

Models for the elastic deformation of honeycombs

A theoretical model has been developed for predicting the elastic constants of honeycombs based on the deformation of the honeycomb cells by flexure, stretching and hinging. This is an extension of earlier work based on flexure alone. The model has been used to derive expressions for the tensile moduli, shear moduli and Poisson's ratios. Examples are given of structures with a negative Poisson's ratio. It is shown how the properties can be tailored by varying the relative magnitudes of the force constants for the different deformation mechanisms. Off-axis elastic constants are also calculated and it is shown how the moduli and Poisson's ratios vary with applied loading direction. Depending on the geometry of the honeycomb the properties may be isotropie (for regular hexagons) or extremely anisotropic. Again, the degree of anisotropy is also affected by the relative magnitude of the force constants for the three deformation mechanisms.     

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.     

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。     

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.     

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     

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.     

The limits of Poisson's ratio in polycrystalline bodies

While it has been established that the elastic moduli and compliances of anisotropic and isotropic materials should be positive for thermodynamic reasons, no condition related to the values of Poisson's ratio has yet been established. However, it is generally accepted that for isotropic materials Poisson's ratio should vary between — 1.0 and 0.5, whereas for orthotropic materials various conditions have been introduced relating the different components of the anisotropic Poisson's ratio with the remaining elastic constants of the material. In this paper, limits for Poisson's ratio of body-centred cubic (bcc) polycrystalline materials are determined, based on the modes of deformation of a typical unit cell of the material subjected to a uniform external loading arbitrarily oriented relative to the principal axes of the crystal. It is shown that the values of Poisson's ratio thus established correlate satisfactorily with experimental values of this constant. The procedure can be readily applied to other structural units of polycrystalline bodies.     

The effect of the processing parameters on the fabrication of auxetic polyethylene

Auxetic (negative Poisson's ratio) ultra high molecular weight polyethylene has been fabricated by a novel thermal processing route consisting of three stages-compaction, sintering and extrusion. In this paper, the sintering stage is examined in detail, the processing window investigated and the optimum conditions to produce the microporous microstructure necessary for a negative Poisson's ratio are identified. The effects of varying the processing parameters are also studied.     

A micromechanics-based gradient model and the effect of high-order stress and particle rolling on localizations for granular materials

This study develops a gradient model to consider heterogeneity of granular materials by means of a thermo-micromechanics method and the hypothesis of kinematics. In this model, the macroscopic variables are related to the micro information by a non-affine projection scheme. Numerical examples illustrated the capability and performance of the presented model in modeling deformation patterns in case of considering particle rolling and not considering particle rolling, and investigated the validity for the stress–strain relation of the presented model.     

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio is explored experimentally as a function of permanent volumetric compression ratio, a processing variable. J _IC values of toughness of negative Poisson's ratio open cell copper foams are enhanced by 80 percent, 130 percent, and 160 percent for permanent volumetric compression ratio values of 2.0, 2.5, and 3.0, respectively, compared to the J _IC value of the conventional foam (with a positive Poisson's ratio). Analytical study based on idealized polyhedral cell structures, approximating the shape of the conventional and re-entrant cells, disclose for re-entrant foam, toughness increasing as Poisson's ratio becomes more negative. The increase in toughness is accompanied by an increase in compliance, a combination not seen in conventional foam, and which may be useful in some applications such as sponges.     

Finding auxetic frameworks in periodic tessellations

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss=-1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE≈-0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.     

Tailoring materials with prescribed elastic properties

This paper describes a method to design the periodic microstructure of a material to obtain prescribed constitutive properties. The microstructure is modelled as a truss or thin frame structure in 2 and 3 dimensions. The problem of finding the simplest possible microstructure with the prescribed elastic properties can be called an inverse homogenization problem, and is formulated as an optimization problem of finding a microstructure with the lowest possible weight which fulfils the specified behavioral requirements. A full ground structure known from topology optimization of trusses is used as starting guess for the optimization algorithm. This implies that the optimal microstructure of a base cell is found from a truss or frame structure with 120 possible members in the 2-dimensional case and 2016 possible members in the 3-dimensional case. The material parameters are found by a numerical homogenization method, using Finite-Elements to model the representative base cell, and the optimization problem is solved by an optimality criteria method.

Numerical examples in two and three dimensions show that it is possible to design materials with many different properties using base cells modelled as truss or frame works. Hereunder is shown that it is possible to tailor extreme materials, such as isotropic materials with Poisson's ratio close to − 1, 0 and 0.5, by the proposed method. Some of the proposed materials have been tested as macro models which demonstrate the expected behaviour.     

Negative Poisson's ratio polyethylene foams

Various polyethylene foams were subjected to thermo-mechanical processing with the aim of transforming them into re-entrant materials exhibiting negative Poisson's ratio. Following transformation, large cell foams (cell sizes of 1 and 2 mm) exhibited re-entrant cell structure and negative Poisson's ratio over a range of processing times and temperatures. Poisson's ratio vs. strain for these foams was similar to prior results for reticulated polyurethane foams. Following processing, microcellular polyethylene foam was densified but cells remained convex; it did not exhibit a substantial negative Poisson's ratio. This foam had a different transition temperature as determined via DSC than the large cell foams.     

GFWRP管增强混凝土柱的轴压泊松比

为完善和发展GFWRP管增强混凝土柱的设计与计算理论,设计并制备了不同管径、壁厚及缠绕角的GWFRP管混凝土柱试件。进行了轴心压缩试验并对试验结果回归分析,得到GFWRP管混凝土柱轴心压缩过程中转折点及峰值点的泊松比变化方程和相应的应变预测公式,得到组合结构轴压全过程的泊松比变化预测方程。可由给定的组分材料性能预测组合构件的极限泊松比和极限应变,达到预测实际工程中GFWRP管混凝土柱抗力与变形性能的目的。通过试验及计算结果对GFWRP管混凝土与传统钢管混凝土的泊松比变化趋势进行了对比分析,发现两者变化规律完全不同。进一步探讨了GFWRP约束管的纤维缠绕角对组合结构轴压泊松比的影响。结果表明,纤维缠绕角与轴压泊松比近似成反比关系。为制定合理的GFWRP复合材料增强混凝土柱规范提供了理论依据。      

Modelling superplastic deformation of materials with a nonequiaxed microstructure

The superplastic deformation behaviour of a two-dimensional nonequiaxed microstructure is investigated on the basis of the grain-rolling mechanism proposed by Paidar and Takeuchi for an equiaxed microstructure. Analysis shows that not only the deformation geometry but also the dynamics of grain boundary dislocation activity will be altered if grains are elongated rather than equiaxed. Constitutive equations thus derived indicate that the grain aspect ratio can impose a remarkable influence on the superplastic stress-strain rate relationship and such an influence can be quite different if the orientation of the applied stress lies over an angle with respect to the longer axis of the grains. The complexity of modelling the superplastic deformation of engineering materials is also discussed.     

特定弹性性能材料的细观结构设计优化

针对具有特定弹性性质的两相复合材料, 研究了特定性能材料优化设计问题的数学模型,提出了基于形状优化的材料设计方法。该方法利用形状优化技术, 设计两相复合材料的细观结构形式, 以使复合材料具有特定的弹性性质。材料的宏观性质由均匀化方法确定。最后给出了零泊松比材料的设计过程和结果。      

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.     

负泊松比复合材料裂纹尖端应力场

具有平面负泊松比的石墨纤维/环氧树脂非平衡层合复合材料具有很高的断裂韧性和缺口断裂强度,这一点已被实验所证实。本文用复变函数——变分方法计算了负泊松比材料裂纹尖端的应力场和应力强度因子,并与常规的平衡复合材料进行了比较。负泊松比材料铺层为[0/15/75/15]s,[0/25/65/25]s;常规复合材料铺层为[0/60/90/-60]s.本文重点研究了主应力方向与纤维方向的夹角以及应力强度因子与断裂韧性的关系。分析结果表明;负泊松比材料的缺口断裂强度高于常规铺层复合材料的缺口断裂强度。      

Measurement of elastic constants using vibrating wire strain gauges on disc and ring specimens

Useful methods of determining elastic constants employing diametrically–loaded disc and ring specimens have been proposed and applied by Durelli and Ferrer. Young's modulus may be measured from tests on a suitably dimensioned ring specimen. Subsequently Poisson's ratio may be found using a disc. The application of the methods described by the authors does not suit the case where the specimens are small and of stiff materials such as metals. In such a case sensitive means are required for measuring change in diameter with light loading. The paper indicates how this can be carried out for an aluminium alloy. The theory relating to the use of the disc for determining Poisson's ratio has been generalised to allow for measurement of change in length over part or all of a diameter. Poisson's ratio of the aluminium alloy was determined with a disc specimen 0.874 in (22.2 mm) diameter, vibrating wire strain gauges on either side of the specimen indicating change in diameter with loading. A ring was subsequently machined from the disc and similarly tested to confirm Young's modulus.