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Abstract

The phenomenon of negative linear compressibility has attracted much interest because of its unusual deformation features with many potential applications. However, the design and fabrication of materials and structures with negative linear compressibility are limited. In this paper, we proposed two approaches to designing and fabricating new composite structures with negative linear compressibility. The effectiveness of the proposed design approaches was validated experimentally by applying uniformly distributed pressure to all surfaces of bulk specimens. The deformation features, strain history, and the effective area reduction of the specimens were analyzed from the experimental data. The results clearly demonstrated the feasibility of the proposed designing and manufacturing approaches for realizing composites with negative linear compressibility.

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... However, the deep understanding the mechanisms of NLC must lead to potential applications as the development of efficient biological structures, nanofluidic actuators or compensators for undesirable moisture-induced swelling of concrete/clay-based engineering materials [313]. Since NLC has been found in systems having a fixed topology, there has been a large amount of work aimed to design NLC materials using topology optimization techniques [211,294,[329][330][331][332]. These techniques are also being used in order to design materials with prescribed bulk, shear or Young moduli, Poisson ratios and other properties [211,294,[329][330][331][332] and may be employed to develop prototypes of a wide series of mechanical devices as bone implants [333]. ...
... Since NLC has been found in systems having a fixed topology, there has been a large amount of work aimed to design NLC materials using topology optimization techniques [211,294,[329][330][331][332]. These techniques are also being used in order to design materials with prescribed bulk, shear or Young moduli, Poisson ratios and other properties [211,294,[329][330][331][332] and may be employed to develop prototypes of a wide series of mechanical devices as bone implants [333]. ...
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... 2,3,9,[22][23][24] Synthetic and design approaches have been developed to obtain materials with improved mechanical performance. 4,9,[25][26][27] However, the number of natural and man-made NLC materials known so far is limited and, for these materials, the magnitude of the negative compressibility and the range of external pressures for which these phenomena are displayed are too small to be widely exploitable in practice. ...
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... Composites have been designed to obtain stronger and tougher materials in various fields since the very early time. 1,2 Many studies have been done on inorganic fillers and organic resin matrix. 3,4 Among them, the interfaces between the filler and matrix is still the key to improvement of the properties of the composites. ...
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... Auxetic materials exhibit uncommon deformation behaviour, e.g., under uniaxial compression (tension), rather than expanding (shrinking) in the lateral direction as conventional materials, auxetic materials would shrink (expand) [1][2][3][4][5][6][7][8][9]. Along with this counter-intuitive behaviour, auxetic materials are regarded to possess many desirable properties, e.g., shear resistance [10,11], indentation resistance [12][13][14][15], fracture resistance [16][17][18][19], synclastic behaviour [20,21], variable permeability [22,23] and energy absorption [24,25]. ...
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In this paper, two kinds of 3D hexagonal honeycomb equivalent models are proposed enlightened by the octahedron model constructed by wine‐rack mechanism. They differ in their unit‐cell arrangement forms which are array and homogeneous arrangements respectively. Referring to the analysis of the octahedron model, the expressions of compressibility properties of the two new models are given and the conditions for obtaining negative compressibility are analyzed. Comparing these two models with the octahedron model, it is found that although the three models are quite different in externality, they have similar mechanical properties (Young's modulus, Poisson's ratio and compressibility) and all have image symmetry in both horizontal directions. Further analysis shows that these three models are so unified that they can be expressed by a more general model, from which we can deduce another model with negative compressibility. Finally, a new method to improve negative compressibility property can be concluded from comparing the three models, that is increasing the number or length of rods without deformation in vertical direction can effectively improve negative compressibility property in this direction and weaken negative compressibility property in the other two directions. This article is protected by copyright. All rights reserved.
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Effective properties and dynamic response of a sandwich panel made of two face sheets and auxetic core are analyzed in this study by computer simulations. The inner composite layer is made of a cellular auxetic structure immersed in a filler material of a given Poisson's ratio (filler material fills the voids in structure). Each cell is composed of an auxetic structure (re-entrant honeycomb or rotating square), i.e., exhibiting negative Poisson's ratio without any filler. Influence of filler material on the effective properties of the sandwich panel is investigated. The proposed structure shows interesting structural characteristics and dynamic properties. Our results clearly show that it is possible to create auxetic sandwich panels made of two solid materials with positive Poisson's ratio. This is even possible if the filler material is nearly incompressible, but can move in out-of-plane direction. Moreover, effective Young's modulus of such sandwich panels becomes very large if the Poisson's ratio of the filler material tends to −1.
Article
There has been considerable interest in materials exhibiting negative or zero compressibility. Such materials are desirable for various applications. A number of models or mechanisms have been proposed to characterize the unusual phenomena of negative linear compressibility (NLC) and negative area compressibility (NAC) in natural or synthetic systems. In this paper we propose a general design technique for finding metamaterials with negative or zero compressibility by using a topology optimization approach. Based on the bi-directional evolutionary structural optimization (BESO) method, we establish a systematic computational procedure and present a series of designs of orthotropic materials with various magnitudes of negative compressibility, or with zero compressibility, in one or two directions. A physical prototype of one of such metamaterials is fabricated using a 3D printer and tested in the laboratory under either unidirectional loading or triaxial compression. The experimental results compare well with the numerical predictions. This research has demonstrated the feasibility of designing and fabricating metamaterials with negative or zero compressibility and paved the way towards their practical applications.
Article
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 was 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.
Article
Materials with unusual mechanical properties can be potentially used as matrices to create high-performance lightweight composites. The appearance of materials with negative Poisson's ratio (auxetics), has led to the evaluation of auxetic composites for possible engineering applications. Because the experimental evaluation of composites with specific properties is expensive and time consuming, computational modelling and simulation provide efficient alternatives to predict the parameters of the composites. In this paper a finite element method was used to find the engineering constants (Young's modulus and Poisson's ratio) of auxetic composites consisting of concentric cylindrical inclusions made of combinations of auxetic and classic (non-auxetic) materials. It has been observed that not only the mechanical properties of the different composite phases influence the effective mechanical properties of the whole composite, but also the location of the same material phases do matter.
Article
The work describes the manufacturing and testing of graded conventional/auxetic honeycomb cores. The graded honeycombs are manufactured using Kevlar woven fabric/914epoxy prepreg using Kirigami techniques, which consist in a combination of Origami and ply-cut processes. The cores are used to manufacture sandwich panels for flatwise compression and edgewise loading. The compressive modulus and compressive strength of stabilized (sandwich) honeycombs are found to be higher than those of bare honeycombs, and with density-averaged properties enhanced compared to other sandwich panels offered in the market place. The modulus and strength of graded sandwich panel under quasi-static edgewise loading vary with different failure mode mechanisms, and offer also improvements towards available panels from open literature. Edgewise impact loading shows a strong directionality of the mechanical response. When the indenter impacts the auxetic portion of the graded core, the strong localization of the damage due to the negative Poisson’s ratio effect contains significantly the maximum dynamic displacement of the sandwich panel.
Article
Exact formulation for calculating effective elastic moduli of an isotropic two-phase disordered composite with ellipsoidal or elliptic inclusions are given in the mean-field approximation, which yields simple analytic expansions of effective Poisson ratio and Young's modulus to second order in the small asphericity parameters for nearly disc-like and spherical inclusions. Analytic expansions to fifth order in these parameters of the depolarizing or demagnetizing factors for nearly spherical ellipsoids have also been obtained, as have those to second order of the critical parameters of the auxeticity windows in the case of rigid auxetic inclusions randomly embedded in an incompressible matrix. For a matrix having a non-negative Poisson ratio, it is found that auxeticity windows for both inclusion volume or area fraction and the ratio of Young's modulus of inclusion to that of a matrix exist only for auxetic inclusions, and a maximum effective Young's modulus occurs at a certain value of volume fraction of auxetic inclusions that are not far from disc-like or spherical. This maximum Young's modulus effect may be exploited to produce technologically important high-strength auxetic composites.
Article
Materials with negative Poisson ratios are known to have high shear rigidities – a useful property for many types of structural and functional materials. To improve upon relatively low Young’s modulus of existing auxetics, one may consider embedding such components in an elastic material with sufficiently high modulus. We show theoretically that such composite materials do exhibit auxeticity when the inclusion volume fraction exceeds a critical value and the ratio of Young’s modulus of inclusion to that of a matrix falls within a definite interval. The existence of these auxeticity windows, once verified experimentally, opens up a new avenue of auxetics research.
Article
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.
Article
Most materials compress axially in all directions when loaded hydrostatically. Contrary to this, some materials have been discovered that exhibit negative linear compressibility and, as such, expand along a specific axis or plane. This paper analyses a fundamental mechanism by using a combination of finite element simulations and analytical derivations to show that negative linear compressibility can be found in a body-centred or face-centred tetragonal network of nodes connected by a network of beams. The magnitude and direction of this behaviour depends on the cross geometry in the network.
Article
The linear compressibility of a solid is defined as the relative decrease in length of a line when the solid is subjected to unit hydrostatic pressure. Materials with a negative linear or area compressibility could have interesting technological applications. However, in the case of homogeneous materials only rare crystal phases exhibit this effect. In particular, for isotropic or cubic solids the linear compressibility is known to be isotropic and positive, namely a sphere of a cubic or isotropic crystal under hydrostatic pressure remains a sphere. For less symmetric solids, it generally varies with the direction n. Here we derive explicit expressions of the stationary values (maximum and minimum) of linear compressibility for single phase solids with monoclinic, orthotropic, tetragonal, trigonal, and hexagonal symmetry. A list of crystals that may exhibit negative linear compressibility in certain directions is outlined. Next, by assembling a two-component material, we propose microstructure networks to achieve such a property. Numerical simulations, based on a refined finite element method, are provided.
Article
The main problem is that of determining the effective moduli for a compressible isotropic elastic medium containing single size, rigid, spherical inclusions at non-dilute concentrations. A solution is synthesized from available rigorous elasticity results that have been found under asymptotic conditions. Preliminary to obtaining this result for the compressible medium case, results are first found for the incompressible case over a range of rigid particle size distributions. All results extend from the dilute condition up through the full packing limit, which depends upon the size distribution.
Article
Materials exhibiting negative linear compressibility display the very unusual and unexpected property of expanding in at least one direction when placed under compressive hydrostatic stress. Here, it is shown that this property may be manifested by systems having high positive Poisson's ratios (non-auxetic), including non re-entrant hexagonal honeycombs and wine-rack models where deformation primarily involves changes in the angles between the ribs of the structures. (C) 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc.
Article
A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poisson's ratio (auxetic), zero Poisson's ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.
Article
A general analytic solution has been obtained to effective Poisson ratio and Young's modulus of an isotropic two-phase disordered composite composed of an incompressible matrix and elliptic or ellipsoidal inclusions, each having a Poisson ratio of −1, in the mean-field approximation, which yields a further result that as long as the inclusion area or volume fraction exceeds 0.33, 0.83, 0.42, 0.61 and 0.85 for nearly disc-, blade-, sphere-, disk- and neddle-like inclusions, respectively, it is always possible to make the resulting composite auxetic. Analytic expansions of the effective elastic moduli in the parameters characterizing a small deviation of inclusion shapes from blades or disks or needles have been developed, giving good approximations when truncated at second order. Similar analytic expansions to fifth order of the depolarizing or demagnetizing factors have also been presented. For a matrix having a non-negative Poisson ratio, it is found that auxeticity windows exist only for auxetic inclusions, and a maximum effective Young's modulus occurs at a certain value of volume fraction of auxetic inclusions that are not far from blade- or disk- or needle-like. This maximum-Young's-modulus effect may be advantageously used to produce technologically important high-strength auxetic composites as in the case of nearly disc-like or spherical inclusions studied before.
Article
The counterintuitive phenomenon of negative linear compressibility (NLC) is a highly desirable but rare property exploitable in the development of artificial muscles, actuators and next-generation pressure sensors. In all cases, material performance is directly related to the magnitude of intrinsic NLC response. Here we show the molecular framework material zinc(II) dicyanoaurate(I), Zn[Au(CN)(2)](2), exhibits the most extreme and persistent NLC behaviour yet reported: under increasing hydrostatic pressure its crystal structure expands in one direction at a rate that is an order of magnitude greater than both the typical contraction observed for common engineering materials and also the anomalous expansion in established NLC candidates. This extreme behaviour arises from the honeycomb-like structure of Zn[Au(CN)(2)](2) coupling volume reduction to uniaxial expansion, and helical Au…Au 'aurophilic' interactions accommodating abnormally large linear strains by functioning as supramolecular springs.
Article
In this work a simple cylindrical structure with a stiff needle-like inclusion embedded within a much softer matrix is presented and analysed with the aim of obtaining a system with tunable thermal expansion properties. It is shown that by the correct combination of the thermal and mechanical properties of the matrix and inclusion, it is possible to design a system which can be tailor-made to exhibit particular values of the coefficient of thermal expansion (CTE) in the radial direction and also negative thermal expansion (NTE). In particular an analytical model to quantify the radial strain with changes in temperature is derived and verified through finite element analysis. The model is used to find correct property combinations which lead to particular values of thermal expansion which could also be negative or zero
Article
Properly designed composite materials can produce thermal expansion coefficients lying well outside the range shown by homogeneous materials both in a single direction and in a plane. Much lower negative values may be produced compared with single materials as well as larger positive values. Such extreme values may be coupled with a choice of other mechanical properties, e.g., Youngs modulus or breaking strength or toughness. In this paper, we demonstrate how to obtain negative values of the expansivity.
Article
The role of negative compressibility is considered in detail. Experimental observations of negative bulk modulus in pre-strained foam are presented and interpreted. A constrained microscopic model which exhibits negative compressibility is proposed. Some other negative and counterintuitive properties of matter, like negative Poisson's ratio, negative thermal expansion, negative specific heat, and negative pressure are also discussed. A simple thermodynamic model with negative thermal expansion is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Article
Composite materials of extremely high stiffness can be produced by employing one phase of negative stiffness. Negative stiffness entails a reversal of the usual codirectional relationship between force and displacement in deformed objects. Negative stiffness structures and materials are possible, but unstable by themselves. We argue here that composites made with a small volume fraction of negative stiffness inclusions can be stable and can have overall stiffness far higher than that of either constituent. This high composite stiffness is demonstrated via several exact solutions within linearized and also fully nonlinear elasticity, and via the overall modulus tensor estimate of a variational principle valid in this case. We provide an initial discussion of stability, and adduce experimental results which show extreme composite behavior in selected viscoelastic systems under sub-resonant sinusoidal load. Viscoelasticity is known to expand the space of stability in some cases. We have not yet proved that purely elastic composite materials of the types proposed and analyzed in this paper will be stable under static load. The concept of negative stiffness inclusions is buttressed by recent experimental studies illustrating related phenomena within the elasticity and viscoelasticity contexts.
Article
We show that KMn[Ag(CN)(2)](3) exhibits the strongest negative linear compressibility (NLC) effect over the largest pressure range yet observed. Variable pressure neutron powder diffraction measurements reveal that its crystal lattice expands along the c axis of its trigonal cell under increasing hydrostatic pressure, while contracting along the a axis. This corresponds to a "wine-rack"-like mechanism for NLC that we find also results in anisotropic negative thermal expansion (NTE) in the same material. Inclusion of extra-framework K(+) counterions has minimal effect on framework flexibility (and hence the magnitude of NTE/NLC) but selectively frustrates the soft phonon modes responsible for destroying NLC in the related material Ag(3)[Co(CN)(6)].
Article
Silver(I) hexacyanocobaltate(III), Ag3[Co(CN)6], shows a large negative linear compressibility (NLC, linear expansion under hydrostatic pressure) at ambient temperature at all pressures up to our experimental limit of 7.65(2) GPa. This behavior is qualitatively unaffected by a transition at 0.19 GPa to a new phase Ag3[Co(CN)6]-II, whose structure is reported here. The high-pressure phase also shows anisotropic thermal expansion with large uniaxial negative thermal expansion (NTE, expansion on cooling). In both phases, the NLC/NTE effect arises as the rapid compression/contraction of layers of silver atoms—weakly bound via argentophilic interactions—is translated via flexing of the covalent network lattice into an expansion along a perpendicular direction. It is proposed that framework materials that contract along a specific direction on heating while expanding macroscopically will, in general, also expand along the same direction under hydrostatic pressure while contracting macroscopically. • negative linear compression • negative thermal expansion • high-pressure • framework materials • flexibility
Article
Rare crystal phases that expand in one or more dimensions when hydrostatically compressed are identified and shown to have negative Poisson's ratios. Some of these crystals (i) decrease volume and expand in two dimensions when stretched in a particular direction and (ii) increase surface area when hydrostatically compressed. Possible mechanisms for achieving such negative linear and area compressibilities are described for single crystals and composites, and sensor applications are proposed. Materials with these properties may be used to fabricate porous solids that either expand in all directions when hydrostatically compressed with a penetrating fluid or behave as if they are incompressible.
Article
When a force deforms an elastic object, practical experience suggests that the resulting displacement will be in the same direction as the force. This property is known as positive stiffness. Less familiar is the concept of negative stiffness, where the deforming force and the resulting displacement are in opposite directions. (Negative stiffness is distinct from negative Poisson's ratio, which refers to the occurrence of lateral expansion upon stretching an object.) Negative stiffness can occur, for example, when the deforming object has stored (or is supplied with) energy. This property is usually unstable, but it has been shown theoretically that inclusions of negative stiffness can be stabilized within a positive-stiffness matrix. Here we describe the experimental realization of this composite approach by embedding negative-stiffness inclusions of ferroelastic vanadium dioxide in a pure tin matrix. The resulting composites exhibit extreme mechanical damping and large anomalies in stiffness, as a consequence of the high local strains that result from the inclusions deforming more than the composite as a whole. Moreover, for certain temperature ranges, the negative-stiffness inclusions are more effective than diamond inclusions for increasing the overall composite stiffness. We expect that such composites could be useful as high damping materials, as stiff structural elements or for actuator-type applications.
Article
A novel foam structure is presented, which exhibits a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.
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