To read the full-text of this research, you can request a copy directly from the authors.
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.
To read the full-text of this research, you can request a copy directly from the authors.
... 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 . 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,. 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, and may be employed to develop prototypes of a wide series of mechanical devices as bone implants . ...
... 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,. 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, and may be employed to develop prototypes of a wide series of mechanical devices as bone implants . ...
The structural and mechanical properties of the deltic, squaric and croconic cyclic oxocarbon acids were obtained using theoretical solid-state methods based in Density Functional Theory employing very demanding calculation parameters in order to yield realistic theoretical descriptions of these materials. The computed lattice parameters, bond distances, angles, and X-ray powder diffraction patterns of these materials were in excellent agreement with their experimental counterparts. The crystal structures of these materials were found to be mechanically stable since the calculated stiffness tensors satisfy the Born mechanical stability conditions. Furthermore, the values of the bulk modulus and their pressure derivatives, shear and Young moduli, Poisson ratio, ductility and hardness indices, as well as mechanical anisotropy measures of these materials were reported. A complete review of the literature concerning the negative Poisson ratio and negative linear compressibility phenomena is given together with the theoretical study of the mechanical behavior of cyclic oxocarbon acid materials. The deltic, squaric, and croconic acids in the solid state are highly anisotropic materials characterized by low hardness and relatively low bulk moduli. The three materials display small negative Poisson ratios. The croconic acid displays the phenomenon of negative linear compressibility for applied pressures larger than ~0.4 GPa directed along the direction of minimum Poisson ratio and undergoes a pressure induced phase transition at applied pressures larger than ~1.0 GPa.
... Such materials are expected to have important applications in extremely sensitive pressure detectors . Current technologies enable manufacturing of various structural motifs to create negative Poisson's ratio  and negative compressibility . Yet, most of the explorations in this field have relied on experiences and intuitions , and rational design of metamaterials with target properties is still a challenge. ...
The origin of negative Poisson's ratio in rutile-type oxides and fluorides is explored through density functional theory (DFT) simulation. The study highlights the dominant role of nearest-neighbor central force interactions, thereby inspiring the design of a new three-dimensional (3D) mechanical metamaterial by mimicking the bond structure via elastic beams. Analytical expressions for the effective Poisson's ratio and compressibility are derived and validated by finite element computations. Numerical results indicate that the material can exhibit simultaneously negative Poisson's ratio and negative linear, area, or volume compressibility. The negative Poisson's ratio is conformed experimentally, and the parametric spaces leading to negative compressibilities are identified explicitly.
... 2,3,9, Synthetic and design approaches have been developed to obtain materials with improved mechanical performance. 4,9, 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. ...
The full crystal structure of the phyllosilicate mineral tuperssuatsiaite, including the positions of the hydrogen atoms in its unit cell, is determined for the first time by using first-principles solid-state methods. From the optimized structure, its infrared spectrum and elastic properties are determined. The computed infrared spectrum is in excellent agreement with the experimental spectrum recorded from a natural sample from Ilímaussaq alkaline complex (Greenland, Denmark). The elastic behavior of tuperssuatsiaite is found to be extremely anomalous and significant negative compressibilities are found. Tuperssuatsiaite exhibits the important negative linear compressibility phenomenon under small anisotropic pressures applied in a wide range of orientations of the applied strain and the very infrequent negative area compressibility phenomenon under external isotropic pressures in the range from 1.9 to 2.4 GPa. The anisotropic negative linear compressibility effect in tuperssuatsiaite is related to the increase of the unit cell along the direction perpendicular to the layers charactering its crystal structure. The isotropic negative area compressibility effect, however, is related to the increase of the unit cell dimensions along the directions parallel to the layers.
... Natural NLC materials are very infrequent . Although synthetic procedures and design approaches have been formulated to obtain materials showing specific elastic properties [1,19,, the magnitude of the NLC and the range of external pressures for which these natural and synthetic materials show NLC are frequently too small to be useable in practice. The purpose of this and the previous studies  is to examine the occurrence of negative mechanical phenomena in organic materials because these effects have been studied only occasionally for this class of compounds, exposing a substantial gap in their research. ...
The crystal structures and elastic properties of the anhydrous zinc and cadmium oxalates and lead oxalate dihydrate are determined using rigorous first-principles solid-state methods. The three materials are shown to display negative Poisson’s ratios (NPR) and to exhibit the negative linear compressibility (NLC) phenomenon. Anhydrous zinc and cadmium oxalates display NLC for a very wide range of external pressures applied in the direction of minimum compressibility in the ranges − 1.3 to 5.5 GPa and − 1.2 to 2.7 GPa, respectively. The increase of volume in both materials is substantial for pressures larger than 3.6 and 1.8 GPa, and the compressibilities become − 70.1 and − 67.0 TPa⁻¹ for pressures of 5.2 and 2.6 GPa, respectively. The increase of volume is so drastic that these materials become unstable for pressures larger than 5.5 and 2.7 GPa. Lead oxalate dihydrate also displays NLC along the direction of minimum Poisson’s ratio for negative pressures in the range − 0.05 to − 0.08 GPa and undergoes a pressure-induced phase transition for relatively low external pressures of the order of 0.1 GPa. The presence of NPR and NLC phenomena in these three materials together with the previous finding of these phenomena for silver oxalate strongly suggests that other metal oxalate materials could also exhibit an extremely anomalous mechanical behavior.
... 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. ...
In the paper, graphene oxide (GO) and two kinds of styrenic resins, poly[styrene-b-(ethylene-co-butylene)-b-styrene] (SEBS) and maleic anhydride (MA) grafted SEBS (MA-g-SEBS), were utilized to explore the interfacial interaction of carbon-based materials and block copolymers as layer-by-layer (LBL) assembly films. The details of the interlayer interaction of the two kinds of composite films were investigated through the analysis of the mechanical properties and internal structure of the composites. For the SEBS/GO composite film, the “interlock” structure tended to form between the GO sheets and SEBS resin, and the physical “interlocking effect” could make full use of the excellent mechanical properties of GO nanosheets. As a result, both failure strength and elongation at break of the SEBS/GO composite film were enhanced by 50 and 25%, respectively. On the other hand, some different structures were found in the MA-g-SEBS/GO composite film, where the GO sheets stacked onto the resin closely because of the chemical interaction between them and no obvious “interlocks” was found within the interface, and the chemical interface interaction was strong enough to prevent the slide of GO nanosheets under tension after the graphene sheets were highly oxidized, so the mechanical properties of the MA-g-SEBS/GO composite film could be also enhanced. Based on an overall consideration of the research results of these LBL assembled composites, choosing more perfect materials and structures is needed, which should use physical and chemical interfacial interactions more efficiently, to obtain better mechanical properties of inorganic carbon–organic resin composites.
... For the last three decades, 2D auxetic metamaterials [13,16,19,21,37,46,82,84,107,152,202,236, were mainly studied. The boom of 3D printing technique facilitated the fabrication of 3D auxetic metamaterials [31,93,241,244,245,, which tremendously released the design freedom of 3D auxetic metamaterials. ...
... 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) . Along with this counter-intuitive behaviour, auxetic materials are regarded to possess many desirable properties, e.g., shear resistance [10,11], indentation resistance , fracture resistance , synclastic behaviour [20,21], variable permeability [22,23] and energy absorption [24,25]. ...
Auxetic materials and structures have received extensive attention due to their unusual behavior. As one of the structures that can realize the auxetic effect, the elliptic perforated structure has been recently developed, but the previous research on the elliptic perforated is limited to the small deformation stage. At the end of the small deformation stage, the elliptic perforated structure becomes dense and loses the auxetic effect. The available compression stroke is very short and therefore the structure has relatively lower specific energy absorption (SEA). In order to make better use of material, through the buckling of lightweight perforated plates, a newly designed re-entrant elliptical perforated structure is proposed in this work. The re-entrant cells rotate and move inward (the first stage), and finally be compressed by neighbor ones (the second stage). Therefore, the structure undergoes rotational deformation in stage one same as previous perforated plates but specific re-entrant deformation in the second stage, thereby realizing the auxeticity in large deformation. Experimental and numerical results show that the stress–strain curve exhibits double platforms, and the novel structure possesses the auxetic effect throughout the whole compression process. Subsequently, a parametric analysis of the re-entrant distance and the ratio of horizontal and vertical wall thickness was carried out for obtaining greater auxetic effect and better stability of the novel re-entrant elliptic perforated structure. The material utilization rate of the re-entrant elliptic perforated plate was greatly improved, and the application prospect of the re-entrant elliptic perforated was also discussed.
To realize extraordinary wave phenomena, metamaterials need to attain unique effective material properties. In this work, we propose an inverse design strategy for metamaterials with specific anisotropic EMD (effective mass density). Although the conventional inverse homogenization technique has been extended to various fields, few works have been published to explore the inverse realization of an EMD tensor, each component of which is supposed to gain a given value at a target frequency. To this end, we propose a calculation scheme, in which the EMD tensor can be calculated in a much similar way to the homogenized static stiffness. Therefore, the scheme is quite convenient for sensitivity analysis. The coating layer interfacing the core and matrix is chosen as the design region because it directly determines the motion of the core. The matrix layout, which not only contributes to the stiffness of the metamaterial but also highly affects the core's local motion, is chosen carefully. The perfect transmodal Fabry–Pérot interference phenomenon is considered in this work, and through several numerical examples, the phenomenon is ideally realized. The proposed design strategy could be critically useful in designing locally resonant metamaterials with general anisotropy.
In our previous work, a monoclinic octahedron model based on the tetragonal octahedron model for the negative compressibility property was analyzed. To design a larger number of new models with greater negative compressibility property, an extensive study to propose the hexagonal and trigonal models constructed by a hinging wine‐rack mechanism is now conducted, according to the concept of the crystal system and the method to design new models by changing the system of models. The compressibility properties through theoretical modeling are analyzed, and the results show that the two models exhibit negative compressibility. Further analysis indicates that the two models have strong similarity with the tetragonal model, which can be analyzed uniformly, and the trigonal model has the greatest negative compressibility property among the three models, irrespective of the on‐axis or off‐axis compressibility property. Finally, owing to the particularity of the space configuration for the hexagonal and trigonal models, a series of new models with different spatial arrangements are proposed, which can greatly increase the number of models with negative compressibility.
A new three-dimensional (3D) cellular model based on hinging open-cell Kelvin structure is proposed for its negative compressibility property. It is shown that this model has adjustable compressibility and does exhibit negative compressibility for some certain conformations. And further study shows that the images of compressibility are symmetrical about the certain lines, which indicates that the mechanical properties of the model in the three axial directions are interchangeable and the model itself has a certain geometric symmetry. A comparison of the Kelvin model with its anisotropic form with the dodecahedron model shows that the Kelvin model has stronger negative compressibility property in all three directions. Therefore, a new and potential method to improve negative compressibility property can be derived by selecting the system type with lower symmetry and increasing the number of geometric parameters.
Enlightened by the concept of crystal system, many of the 3D models with negative compressibility that have been proposed so far are cellular models with periodic arrays, which can be called as orthogonal models or tetragonal models. Therefore, a more effective method to design 3D models with negative compressibility by changing the system type of the existing models can be developed. In this work, a monoclinic octahedron model based on the tetragonal octahedron model studied previously is proposed and its compressibility property is analyzed in detail through theoretical modeling. The specific conditions for the model to obtain negative compressibility are given in the discussion of on‐axis mechanical properties. The study about off‐axis compressibility shows that in addition to the geometric features, the measuring direction of compressibility and the arrangement of framework may also have a great influence on negative compressibility effect of the model. This article is protected by copyright. All rights reserved.
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.
Negative linear compressibility (NLC) is a rare high-pressure observation that lattice contraction is accompanied by the structural expansion along a specific direction. Generally, this counterintuitive phenomenon only derives from the intrinsic structural characteristics of materials and cannot be tuned by external perturbations. Searching for an effective method to control NLC effect is still a challenge in both chemical and material science. Here, we successfully discover and select the NLC behaviors in the metal-organic framework (MOF) of [Cu(4,4'-bpy)2(H2O)2]·SiF6 (Cu(bpy)·SiF) through controlling the pressure conditions therein. The NLC effect of Cu(bpy)·SiF originates from the wine-rack mechanism that quasi-square grids transfer to rhombic ones with the structural expansion along the diagonal direction at high pressure. Meanwhile, both of the pressure range and magnitude of the NLC responses are enlarged with optimized pressure conditions. This study not only presents the intriguing selected NLC behaviors of a MOF but also proves the effects of pressure conditions on NLC, which offers promising strategies for further design and applications of NLC materials.
In this paper, an efficient concurrent optimization method of macrostructures, and material microstructures and orientations is proposed for maximizing natural frequency. It is assumed that the macrostructure is composed of uniform material with the same microstructure but with various orientation. The bi-directional evolutionary structural optimization (BESO) method is applied to optimize the macrostructure and its material microstructure under a given weight constraint. Meanwhile, the optimality condition with respect to local material orientation is derived and embedded in the two-scale design of macrostructures and material microstructures. Numerical examples are presented to demonstrate the capability and effectiveness of the proposed optimization algorithm. The results show that the current design of macrostructures, material microstructures, and local material orientation greatly improves structural dynamic performance.
Three 3D models with negative compressibility have been presented in our previous paper [X. Q. Zhou et al., Phys. Status Solidi B 2016, 253, 1977]. However, the 2D mechanism (i.e., wine‐rack mechanism) which we used to design 3D models is so symmetrical that the axial properties of it are equivalent, so we have only focused on geometry features. In this work, an extended study is conducted in order to find a more efficient method to design 3D structures with evident negative compressibility. Through theoretical modeling, the compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for negative compressibility to be exhibited are discussed. The study shows that in addition to the geometry features, negative compressibility effects can also be significantly affected by the arrangement of the framework and layout orientations of 2D mechanism. The compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for the negative compressibility to be exhibited are discussed. It is shown that in addition to the geometry features which have already been widely discussed, the arrangement of the framework and the layout orientations of 2D mechanisms can also have a great influence on the negative compressibility effect.
We have investigated anomalous lattice behavior of metal organic framework compound AgC8N5on application of pressure and temperature using ab-initio density functional theory calculations. The van der Waals dispersion interactions are found to play an important role in structural optimization and stabilization of this compound. Our ab-initio calculations show negative linear compressibility (NLC) along the c-axis of the unit cell. The ab-initio lattice dynamics as well as the molecular dynamics simulations show large negative thermal expansion (NTE) along the c-axis. The mechanism of NLC and NTE along the c-axis of the structure is governed by the dynamics of Ag atoms in the a-b plane. The NLC along the c-axis drives the NTE along that direction.
Elastic instability has been increasingly used to design buckling-induced auxetic metamaterials. However, only limited patterns of existing three dimensional (3D) buckling-induced auxetic metamaterials exhibit a reliable 3D auxetic behaviour, i.e., the material will contract along two normal lateral directions under compression along the third direction. In this paper, we study a simple geometrical shape for achieving 3D auxetic behaviour. The unit cell of the proposed 3D design is composed of a solid sphere and three cuboids. Two representative models, one with slender connecting bars and the other with thick connecting bars, are investigated both numerically and experimentally. The results indicate that the designed material with thick connecting bars did not exhibit auxetic behaviour while the one with slender connecting bars did. However, the anticipated 3D auxetic behaviour degraded to a two dimensional (2D) auxetic behaviour, i.e., the material would contract only in one lateral direction and maintain nearly the same dimension in the other lateral direction. This finding was further confirmed by experiments. This research has demonstrated challenges in designing and manufacturing of buckling-induced auxetic metamaterials with 3D auxetic behaviour and highlighted the importance of optimising and fine-tuning the auxetic unit cell using the pattern scale factor.
Foam must be engineered to absorb a particular range of energy in various impact-related applications. Since energy absorption is dependent upon the unique stress-strain response of each foam specimen, it is difficult to quantify analytically; thus, energy absorption cannot be easily compared across materials. Current methods accomplish this using an experimental approach, individually testing foam materials, densities, and geometries to quantify how each influences energy absorption. Such methods require large amounts of time and money to characterize a narrow range of foams. This paper facilitates foam selection by deriving generalized energy absorption material indices. Assuming Euler buckling of columns in the open-cell foam structure, this paper applies equations derived by Maiti et al. to a typical impact scenario wherein the indices are extracted. Using existing Ashby charts, these indices allow polymers to be ranked by the mass and cost each would require as a foamed structure to satisfy specific energy absorption constraints. The presented method allows the energy absorption of a wide range of flexible foams to be compared and relieves the need for extensive factor-specific testing. This method is applied to football helmet foam selection; however, it can be used for many applications where energy absorption is of interest.
Metallic auxetic metamaterials are of great potential to be used in many applications because of their superior mechanical performance to elastomer based auxetic materials. Due to the limited knowledge on this new type of materials under large plastic deformation, the implementation of such materials in practical applications remains elusive. In contrast to the elastomer based metamaterials, metallic ones possess new features as a result of the nonlinear deformation of their metallic microstructures under large deformation. The loss of auxetic behaviour in metallic metamaterials led us to carry out a numerical and experimental study to investigate the mechanism of the observed phenomenon. A general approach was proposed to tune the performance of auxetic metallic metamaterials undergoing large plastic deformation using buckling behaviour and the plasticity of base material. Both experiments and finite element simulations were used to verify the effectiveness of the developed approach. By employing this approach, a 2D auxetic metamaterial was derived from a regular square lattice. Then by altering the initial geometry of microstructure with the desired buckling pattern, the metallic metamaterials exhibit auxetic behaviour with tuneable mechanical properties. A systematic parametric study using the validated finite element models was conducted to reveal the novel features of metallic auxetic metamaterials undergoing large plastic deformation. The results of this study provide a useful guideline for the design of 2D metallic auxetic metamaterials for various applications.
Negative linear compressibility (NLC) is still considered an exotic property, only observed in a few obscure crystals. The vast majority of materials compress axially in all directions when loaded in hydrostatic compression. However, a few materials have been observed which expand in one or two directions under hydrostatic compression. At present, the list of materials demonstrating this unusual behaviour is confined to a small number of relatively rare crystal phases, biological materials, and designed structures, and the lack of widespread availability hinders promising technological applications. Using improved representations of elastic properties, this study revisits existing databases of elastic constants and identifies several crystals missed by previous reviews. More importantly, several common materials—drawn polymers, certain types of paper and wood, and carbon fibre laminates—are found to display NLC. We show that NLC in these materials originates from the misalignment of polymers/fibres. Using a beam model, we propose that maximum NLC is obtained for misalignment of 26°. The existence of such widely available materials increases significantly the prospects for applications of NLC.
High-resolution powder diffraction data have been recorded on cubic ZrW2O8 [a = 9.18000 (3) Å at 2 K] at 260 temperatures from 2 to 520 K in 2 K steps. These data have confirmed that α-ZrW2O8 has a negative coefficient of thermal expansion, α = −9.07 × 10−6 K−1 (2–350 K). A `parametric' approach to Rietveld refinement is adopted and it is demonstrated that a full anisotropic refinement can be performed at each temperature, despite using a data collection time of only 5 min. Examination of the resulting structural parameters suggests that the origin of the contraction with increasing temperature can be traced straightforwardly to the rigid-body transverse librations of bridging O atoms. α-ZrW2O8 undergoes a phase transition from P213 to Pa3¯ at 448 K that is associated with the onset of considerable oxygen mobility. The phase transition can be described in terms of a simple cubic three-dimensional Ising model. Unusual kinetics are associated with this phase transition. Hysteresis in the cell parameter through the phase transition is the opposite of that normally observed.
Negative compressibility is the ability to expand in at least one dimension rather than shrinking upon the application of an externally applied hydrostatic pressure. It is shown that, contrary to current perception, negative linear compressibility may be obtained from re-entrant hexagonal truss systems of specific geometric features which deform through non-equal changes in the lengths of the cell walls when deforming through a constrained angle stretching rather than other modes of deformation (such as flexure or hinging, modes of deformation that also lead to auxetic behaviour in honeycombs). Negative compressibility is predicted in the vertical direction for particular re-entrant geometries of this smart hexagonal truss system when the vertical ribs are much stiffer than the inclined ribs.
Mean-field theory of elastic moduli of a two-phase disordered composite with ellipsoidal inclusions is reviewed together with an indication as to how interactions among inclusions may be taken into account. In the mean-field approximation, the effective Poisson ratio σe in composites with auxetic inclusions of various shapes such as discs, spheres, blades, needles, and disks is studied analytically and numerically. It is shown that phase properties such as inclusion volume or area fraction φ and matrix and inclusion Poisson ratios (σm and σ) and Young’s moduli (Em and E) have a marked effect on σe. The earlier theoretical findings of the existence of auxeticity windows and the widening effect of inclusion-inclusion interactions on the window for δ=E/Em are reconfirmed for composites of auxetic spheres in both two and three dimensions, with new auxeticity windows discovered for the other inclusion shapes. For a composite with σ=-0.8, σm=0.25, and φ=0.4, it is found that the sphere is the most σe-lowering or negative-σe-producing inclusion shape for δ around 1/2, while disklike inclusions yield a most negative σe for δ greater than 1.
Several typesof actuation processes for carbon nanotubes, including non-Faradaic actuation by double-layer charge injection, electrostatic actuation, and light-driven actuation were reported. Thus, it was investigated whether large actuator strains can be obtained at extreme electrochemical potentials for carbon nanotube sheets. The result was the discovery of a new actuation mechanism that generates actuator stains of up to 300% in the thickness direction of carbon nanotube sheets.
When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilizations of (meta)stable equilibria of the constituents. These destabilizations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micromechanical controls, and protective devices.
Improved electrically powered artificial muscles are needed for generating force, moving objects, and accomplishing work.
Carbon nanotube aerogel sheets are the sole component of new artificial muscles that provide giant elongations and elongation
rates of 220% and (3.7 × 104)% per second, respectively, at operating temperatures from 80 to 1900 kelvin. These solid-state–fabricated sheets are enthalpic
rubbers having gaslike density and specific strength in one direction higher than those of steel plate. Actuation decreases
nanotube aerogel density and can be permanently frozen for such device applications as transparent electrodes. Poisson's ratios
reach 15, a factor of 30 higher than for conventional rubbers. These giant Poisson's ratios explain the observed opposite
sign of width and length actuation and result in rare properties: negative linear compressibility and stretch densification.
Composites with negative stiffness inclusions in a viscoelastic matrix are shown to have higher stiffness and mechanical damping tandelta than that of either constituent and exceeding conventional bounds. The causal mechanism is a greater deformation in and near the inclusions than the composite as a whole. Though a block of negative stiffness is unstable, negative stiffness inclusions in a composite can be stabilized by the surrounding matrix. Such inclusions may be made from single domains of ferroelastic material below its phase transition temperature or from prebuckled lumped elements.
Here three analytical models are presented through the layout of wine-rack mechanism in three dimensions (3D) where the conditions for these models to exhibit an extraordinary property, i.e. negative compressibility are specified. In particular, we show that these three models have adjustable compressibility that can be tailored for specific applications and can exhibit NLC, NAC, zero and negative Poisson's ratios in some cases. In this way, the potential of this 2D mechanism in designing 3D models with anomalous properties can be brought out.
Composites with elliptic inclusions of long semi-axis a and short semi-axis b are studied by the Finite Element method. The centres of ellipses form a square lattice of the unit lattice constant. The neighbouring ellipses are perpendicular to each other and their axes are parallel to the lattice axes. The influence of geometry and material characteristics on the effective mechanical properties of these anisotropic composites is investigated for deformations applied along lattice axes. It is found that for anisotropic inclusions of low Young's modulus, when a + b → 1 the effective Poisson's ratio tends to -1, while the effective Young's modulus takes very low values. In this case the structure performs the rotating rigid body mechanism. In the limit of large values of Young's modulus of inclusions, both effective Poisson's ratio and effective Young's modulus saturate to values which do not depend on Poisson's ratio of inclusions but depend on geometry of the composite and the matrix Poisson's ratio. For highly anisotropic inclusions of very large Young's modulus, the effective Poisson's ratio of the composite can be negative for nonauxetic both matrix and inclusions. This is a very simple example of an auxetic structure being not only entirely continuous, but with very high Young's modulus. A severe qualitative change in the composite behaviour is observed as a/b reaches the limit of 1, i.e. inclusions are isotropic. The observed changes in both Poisson's ratio and Young's modulus are complex functions of parameters defining the composite. The latter allows one to tailor a material of practically arbitrary elastic parameters.
Negative Poisson's ratio has already been discovered for many geometrical structures. In most cases, however, the metamaterials built upon such geometries are foams or cellular solids. In this paper, a unidirectional fibrous composite built of two constituent materials of different thermomechanical properties has been studied. The resultant composite is a solid material in its volume. In order to obtain a material of the required properties, both the geometry of fibers and the influence of temperature on both materials have been investigated.
As an effective candidate for enhancing energy absorption, a range of foam materials have gained considerable popularity, in which the density, Young's modulus and plasticity of foam materials are considered critical to crashworthiness. Relatively speaking, less attention has been paid to the roles played by the Poisson's ratio of foam or cellular materials. More importantly, the interaction between different Poisson's ratios and thin-walled structures has been a critical yet under-studied issue. This paper aims to explore the effects of negative, zero and positive Poisson's ratio of auxetic foams, ranging from À1 to 0.5, on structural crashworthiness and seek optimal design for different foam-filled square, circular and conic tubes. In this study the specific energy absorption (SEA) and mean crushing force (MCF) are taken as the objective functions by using mathematical regression analysis. The sequential quadratic programming (SQP) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are employed for single and multiobjective design of foam-filled tubes with different Poisson's ratios, respectively. The optimal Poisson's ratio is obtained for these three different types of foam-filled tubes. By comparison we found that the crashworthiness of foam filled conic tube is the best, followed by circular and then squared tubes. The study provides new insights into material selection and design with a more favorable Poisson's ratio for crashworthiness.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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)].
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
• framework materials
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.
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.
Lett. 2001, 86, 2897-2900, doi:10.1038/35069035, Available online:
Negative linear compressibility: beyond the wine-rack model and towards engineering applications
Barnes, D 2017, Negative linear compressibility: beyond the wine-rack model and towards
engineering applications, PhD thesis, university of Exeter press, University of Exeter
A C C E P T E D
M A N U S C R I P T
A A Poźniak
K W Wojciechowski
J N Grima
A.A. Poźniak, K.W. Wojciechowski, J.N. Grima, L. Mizzi, Planar auxeticity from elliptic
inclusions, Compos. Part B-Eng. 94 (2016) 379–388 http://dx.doi.org/10.1016/j.
compositesb.2016.03.003 Available online: http://www.sciencedirect.com/science/
The compressibility of metals at high pressures, P. Natl. Acad. Sci. USA 8 (1922) 361-365 Available online: https
P W Bridgman
P.W. Bridgman, The compressibility of metals at high pressures, P. Natl. Acad. Sci.
USA 8 (1922) 361-365 Available online: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1085188/.
Composites with needle-like inclusions exhibiting negative thermal expansion: a preliminary investigation Composite materials of controlled thermal expansion
J N Grima
R J Stearn
L N Mccartney
J.N. Grima, B. Ellul, D. Attard, R. Gatt, M. Attard, Composites with needle-like inclusions exhibiting negative thermal expansion: a preliminary investigation, Compos.
Sci. Technol. 70 (2010) 2248-2252 http://dx.doi.org/10.1016/j.compscitech.2010.
 A. Kelly, R.J. Stearn, L.N. McCartney, Composite materials of controlled thermal expansion, Compos. Sci. Technol. 66 (2006) 154-159 http://dx.doi.org/10.1016/j.
compscitech.2005.04.025 Available on: http://www.sciencedirect.com/science/article/pii/S0266353805001338.
Negative Linear Compressibility: Beyond the Wine-rack Model and Towards Engineering ApplicationsPhD thesis
D. Barnes, Negative Linear Compressibility: Beyond the Wine-rack Model and Towards Engineering ApplicationsPhD thesis University of Exeter Press, University of
Development of novel auxetic structures based on braided composites
D V Oliveira
P. Subramani, S. Rana, D.V. Oliveira, R. Fangueiro, J. Xavier, Development of novel
auxetic structures based on braided composites, Mater. Des. 61 (2014) 286-295
http://dx.doi.org/10.1016/j.matdes.2014.04.067 Available online: http://www.