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Simple cubic three-dimensional auxetic metamaterials

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Abstract

Elastic instability of soft cellular solids plays an increasingly important role in the creation of metamaterials with smart properties. Inspiration for much of this research comes from a planar metamaterial with negative Poisson's ratio behavior induced by elastic instability. Here we extend the concept of buckling induced pattern switch further to the design of a new series of three-dimensional metamaterials with negative Poisson's ratio over a large strain range. The highlight of this work is that our designs are based on very simple initial geometric shapes.Different deformation patterns of materials without and with auxetic behavior.

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... Contrary to conventional materials which show a positive Poisson's ratio, auxetic materials contract laterally when compressed vertically or expand laterally when elongated vertically [2,3]. Auxetic materials have been an extremely hot topic over the past few years, and auxetic behavior has been achieved by different types of materials such as metals [4][5][6], ceramics [7,8], polymers [9][10][11][12][13], and composites [14,15]. ...
... this type of structures to achieve auxetic behavior. For those commonly used polymers, varying geometrical features of the centrosymmetric chiral structure considerably affects the mechanical properties of the constituted auxetic materials in a large range regarding the stiffness [4,10,29], strength [4,10,29] and deformation localization [30,31] which is the mechanism of NPR behavior. For cementitious materials, similar influence can be identified from the preliminary study by [28]. ...
... this type of structures to achieve auxetic behavior. For those commonly used polymers, varying geometrical features of the centrosymmetric chiral structure considerably affects the mechanical properties of the constituted auxetic materials in a large range regarding the stiffness [4,10,29], strength [4,10,29] and deformation localization [30,31] which is the mechanism of NPR behavior. For cementitious materials, similar influence can be identified from the preliminary study by [28]. ...
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This research presents an investigation of the compressive behavior of auxetic cementitious cellular composites (CCCs) using a combination of experiments and finite element (FE) simulations. Typical auxetic centrosymmetric geometry was used as unit cells for the cellular structure and fiber reinforced cementitious mortar were used as constituent material. By varying the cellular geometry, three CCCs (P0, P25 and P50) were prepared then experimentally and numerically tested under uniaxial compression with different boundary conditions. Good agreement can be found between experimental and FE simulated results: Only CCCs with chiral section (P25 and P50) exhibited auxetic behavior and a typical compressive stress-strain response with two peaks was found; Under restrained boundary condition, different from the cone confinement zone observed in bulk cementitious materials, re-entrant confinement zone was found in the auxetic CCCs. More importantly, a cracking initiated section rotation mechanism is identified for the CCCs’ auxetic behavior which is distinct from the elastic instability mechanism of polymeric auxetic materials with the same cellular structure. In terms of density, energy dissipation ability and Poisson’s ratio, the auxetic CCCs shows excellent properties making them promising in various civil engineering applications.
... The 3D anti-tetrachiral (3ATC) design studied here has been described previously [4,5] ( Fig. 1 a), and belongs to a family of similar auxetic structures [43][44][45][46] . The geometry is basically made up of a chiral sub-unit cell which has plane projections equivalent to the 2D antitetrachiral structure [37] ( Fig. b). ...
... Truss IV is distinguished from Truss II to highlight that it is a different lateral truss, in another plane. Because of this offset, there will be an out-of-plane rotation of the cube in the X-Z plane, , which adds a lateral displacement of approximately e to Eq. (44) . ...
... Similarly, geometries involving distal horizontal trusses, as well as "same-plane " configurations, exhibit higher E values because of stricter constraints. This can be observed from Eqs. (44) and Eq. (A7) (refer to Fig. 9. Calculated trends for the fraction of overall lattice strain that is contributed by joint rotation, f rot , vs (a) strain, for the geometry where e/a = 2/3, w/a = 1/3, L/a = 10/3 (b) relative density, / s , which was varied through L/a for 3 different e/a values and (c) relative density, varied through w/a for 3 different L/a values. ...
Article
The elastic modulus and Poisson's ratio of a 3D anti-tetrachiral (3ATC) metamaterial design was investigated using an exact analytical model, finite element simulations and experiments on additively manufactured Ti6Al4V lattices. The 3ATC structure was found to undergo a unique symmetric-to-asymmetric transition as the number of unit cells in the lattice decreases, an observation that has not been reported to date. A reduced lattice size also increases the influence of shear forces introduced by the fixed boundary conditions, which can lead to a higher elastic modulus in certain orientations and reduce it in others. These shear forces also drive the joints in small lattices into an out-of-plane rotation that causes the Poisson's ratio of such structures to range from-1.2 to 1 for different relative densities, in contrast to a constant value of-0.5 for bulk 3ATC lattices that do not undergo this joint twisting. Our results strongly indicate that the 3ATC structure belongs to a new 'rotation-dominated' geometric class in the Ashby framework for cellular materials, in addition to the well-established bending-and stretch-dominated topologies. The main contributor of strain for this class of materials is rigid joint rotation, with novel, distinctive traits such as a nonlinear elastic stress-strain response and multiple relative modulus vs. relative density relationships. For the 3ATC structure, one of these relations is linear, similar to stretch-dominated structures, while the other is disjointed and does not follow the power law, which is atypical of a cellular material.
... The existing material models of PolyJet elastomers in the literature are widely inconsistent as their time-dependency is often oversimplified [27,28] or entirely overlooked [29][30][31][32][33]. A recent study collected the shear modulus of several of the existing material models for T+ and reported a variation from 0.158-0.330 ...
... MPa [27]. Reasons for this could be that studies regarded Tango (T) and T+ as linear elastic [33,34] or purely hyperelastic using Neo-Hookean [30] or Arruda-Boyce material models [35], disregarding their time-dependent behaviour. The majority of studies which have explored PolyJet elastomers have focused on their time-independent behaviour [14,27,36]. ...
Article
Material jetting, particularly PolyJet technology, is an additive manufacturing (AM) process which has introduced novel flexible elastomers used in bio-inspired soft robots, compliant structures and dampers. Finite Element Analysis (FEA) is a key tool for the development of such applications, which requires comprehensive material characterisation utilising advanced material models. However, in contrast to conventional rubbers, PolyJet elastomers have been less explored leading to a few material models with various limitations in fidelity. Therefore, one aim of this study was to characterise the mechanical response of the latest PolyJet elastomers, Agilus30 (A30) and Tango+ (T+), under large strain tension-compression and time-dependent high-frequency/relaxation loadings. Another aim was to calibrate a visco-hyperelastic material model to accurately predict these responses. Tensile, compressive, cyclic, dynamic mechanical analysis (DMA) and stress relaxation tests were carried out on pristine A30 and T + samples. Quasi-static tension-compression tests were used to calibrate a 3-term Ogden hyperelastic model. Stress relaxation and DMA results were combined to determine the constants of a 5-term Prony series across a large window of relaxation time (10 μs - 100 s). A numerical time-stepping scheme was employed to predict the visco-hyperelastic response of the 3D-printed elastomers at large strains and different strain rates. In addition, the anisotropy in the elastomers, which stemmed from build orientation, was explored. Highly nonlinear stress-strain relationships were observed in both elastomers, with a strong dependency on strain rate. Relaxation tests revealed that A30 and T + elastomers relax to 50% and 70% of their peak stress values respectively in less than 20 seconds. The effect of orientation on the loading response was most pronounced with prints along the Z-direction, particularly at large strains and lower strain rates. Moreover, the visco-hyperelastic material model accurately predicted the large strain and time-dependent behaviour of both elastomers. Our findings will allow for the development of more accurate computational models of 3D-printed elastomers, which can be utilised for computer-aided design in novel applications requiring flexible or rate-sensitive AM materials.
... The normal behaviour of hard contact and the contact domain of all with self were set for the contact property. The material was set as soft isotropic elastic rubber with reference to our previous work (Shen et al., 2014). The material properties were as follows: Young's modulus is 1 MPa, the density is 1,040 Kg/m 3 and the Poisson's ratio is 0.47. ...
... The material properties were as follows: Young's modulus is 1 MPa, the density is 1,040 Kg/m 3 and the Poisson's ratio is 0.47. The tangential behaviour of penalty friction formulation is used and the friction coefficient is 0.15 (Shen et al., 2014). To minimize the influence of inertia, an amplitude of smooth step was applied on the top layer of the models to guarantee zero acceleration at the beginning of the load. ...
Article
Purpose This paper aims to study the tensile performance, deformation characteristics, auxeticity and stability of different auxetic tubular structures generated by cutting method and pattern scale factor (PSF) method using validated finite element analysis. Design/methodology/approach Two types of auxetic tubular structures were designed by a coordinate transformation method and the PSF adjustment method, respectively. ABAQUS/explicit solver was used for the large deformation analysis and the displacement of key nodes was extracted to calculate Poisson’s ratio value and evaluate the deformation of tubular structures. Findings The random cut method was not suitable for designing auxetic tubular structures. Vertical and horizontal cut approach was suitable, but the change of the tubular diameter was lower than the tubular structures generated by the PSF adjustment method. Research limitations/implications Simple ways to generate auxetic tubular structure, which can be made into intelligent and foldable equipment, such as annuloplasty rings, angioplasty stents and oesophageal stents. By combined with shape memory polymer, various smart tubular materials and structures with various functions can be designed, especially in medical scaffold and other medical equipment fields. Originality/value The auxetic characteristic of tubular structure designed by using random cut method has been investigated for the first time. The outcome of this study would be very useful design tubular structures with better mechanical properties.
... A buckling analysis is performed to determine if a desired buckling mode exists. The microstructure of the material could then be initially imperfected by the introduction of this buckling mode [106]. ...
Article
Meta-biomaterials are designer biomaterials with extraordinary characteristics that originate from their geometrical designs. Additive manufacturing (AM) is a perfect fabrication route for manufacturing such meta-biomaterials due to its excellent characteristics. The present paper aims to provide a critical review of the research in the domain of additively manufactured meta-biomaterials. Total 390 research papers published during the last 30 years, 1991 to 2021, are reviewed. Literature review related to additively manufactured meta-biomaterials is classified into five sections- (i) methodology of design, (ii) materials, (iii) AM techniques, (iv) properties, and (v) biomedical applications. The novelty of the present review paper is to provide a roadmap for future research in the domain of additively manufactured meta-biomaterials. As a result of the suggested research, a sophisticated patient-specific additively manufactured meta-biomaterial with the necessary qualities will be developed in the shortest period possible.
... Hence, auxeticity has been observed at different scales, from macro-to nano-dimensions. Apart from examples of natural materials with an intrinsic negative Poisson's coefficient [2][3][4][5], auxetic media are generally artificiallymade systems whose microstructure is designed by exploiting different geometries and mechanisms: re-entrant unit cells [6][7][8][9], star-shaped inclusions [10,11], chiral configurations [12][13][14][15], double arrowhead honeycombs [16], perforations and cuttings [17][18][19][20][21], rotating rigid units [22], lattices [23][24][25] and elastic instabilities [26,27]. Alternative approaches to design auxetic media are presented in the reviews [28][29][30][31][32]. ...
Preprint
Full-text available
We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes the medium isotropic in the plane. Remarkably, the mesoscale interaction between the first- and second-level cuts enables the attainment of a value of the Poisson's ratio close to the minimum reachable limit of -1. The effective properties of the hierarchical auxetic structure are determined numerically, considering both a unit cell with periodic boundary conditions and a finite structure containing a large number of repeating cells. Further, results of the numerical study are validated experimentally on a polymeric specimen with appropriately arranged rank-two cuts, tested under uniaxial tension. We envisage that the proposed hierarchical design can be useful in numerous engineering applications exploiting an extreme auxetic effect
... However, these natural examples are rare; hence, artificially designed geometries, leading to auxetic behavior, have been proposed in the literature. The latter are mainly based on the following mechanisms: reentrant structures [34][35][36][37][38][39], star-shaped inclusions and pores [40,41], chirality [34,[42][43][44][45][46][47][48][49], rotating units [50,51], pores and cuts [52][53][54][55][56][57][58][59], instabilities [60][61][62], two-dimensional and threedimensional lattices [63][64][65], and other approaches [66][67][68][69][70][71][72]. ...
Article
In this article, effective properties of Miura-ori patterned sheets are studied. The thickness of the facets is allowed to have considerably large values; hence, the structural response of the system cannot be determined by considering only the kinematics of the folding. In particular, large negative values of the Poisson’s ratio have been observed for particular sets of parameters. Numerical outcomes, for periodic and finite systems, have been validated by an experimental campaign, where several specimens with different geometries and materials have been tested. The elastic fields of the specimens have been measured with the digital image correlation method.
... In particular, seismic metamaterials are employed to enhance the antiseismic behavior of buildings [15][16][17]. Moreover, acoustic metamaterials are used to transform acoustic waves and low frequency vibrations into electrical power [18][19][20][21], while metamaterials performing invisible frequencies are used to enhance the efficiency of solar cells [22][23][24]. Additionally, metamaterial sensors are used to detect thermal fluctuations and changes in order to optimize temperature control in a building [25][26][27]. ...
Preprint
Full-text available
Energy self sufficiency, as well as optimal management of power in buildings is gaining importance, while obtaining power from traditional fossil energy sources is becoming more and more expensive. In this context, millimeter scale metasurfaces can be employed to harvest energy from microwave sources. They can also be used as sensors in the microwave regime for efficient power management solutions. In the current study, a simple spray printing method is proposed to develop metasurfaces in construction materials, i.e., plasterboard and wood. Such materials are used in the interior design of buildings; therefore, the implementation of metasurfaces in large areas, such as walls, doors and floors, is realized. The fabricated metasurfaces were characterized regarding their electromagnetic performance. It is hereby shown that the investigated metasurfaces exhibit an efficient electromagnetic response in the frequency range 4 to 7 GHz, depending on the MS. Thus, spray printed metasurfaces integrated on construction materials can potentially be used for electromagnetic applications, for buildings power self efficiency and management.
... Topologies related to mechanical metamaterials largely involve the use of lattices and/or multiphase composites, as well as applying patterns of perforations to convert conventional materials substrates into architected materials. Examples of classes of metamaterials systems include hexagonal lattices [1], rotating rigid units (rotating squares, rectangles, parallelograms, rhomboidal, triangles, cubes, and hierarchical mixed topologies) [2][3][4][5][6][7][8][9][10][11][12][13], chiral pattern formations [14], as well as re-entrant configurations [15]. Regular or random slits/cuts have also been adopted to generate unusual mechanical behaviour in mechanical metamaterials [16][17][18][19]. ...
Preprint
We describe the out-of-plane bending of chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.
... Lattice metamaterials have attracted great attention during the recent decade due to their capacity in tunable mechanical properties and counterintuitive properties when compared with natural materials, such as negative Poisson's ratio [1][2][3] and negative thermal expansion [4][5][6]. They are usually composed of periodic "unit cells" which derive from ingenuously designed microstructure [7,8]. The periodically arranged design concept is similar to natural crystal lattice structures [9,10]. ...
Article
Full-text available
Lattice structure metamaterials generally exhibit better stiffness and/or tunable properties than natural materials. They have important applications in mechatronics and tissue engineering areas. In this work, we demonstrate crystal structure-inspired body-centered cubic (BCC)-lattice architected structures using different acrylate-based polymer materials to study the mechanical response in large deformation. Rigid BCC lattice metamaterials manifest outstanding recovery properties after undergoing multi-cycle compression. With appropriate cell wall thickness, the lattices have the capacity to recover their original shape and maintain a degree of stiffness. In further exploration, we combined mechanical tests and digital image correlation to elaborate on the deformation mechanisms. The digital image correlation (DIC) proves that displacement discrepancy exists in local positions. We propose hourglass and twist models to describe the buckling-induced pattern transformation which occurs during cyclic compressive deformation using simulation.
... Potential applications of metamaterials are diverse, including metamaterial antennas [1][2][3], metamaterial absorbers [4][5][6], metamaterial cloaking devices [7][8][9], and metamaterial sound filtering [10][11][12], etc. Auxetic metamaterials, known as a special type of mechanical metamaterials, exhibit a negative Poisson's ratio property, as they can expand (contract) in a transverse direction when uniaxially stretched (compressed) [13][14][15][16]. Besides, auxetic metamaterials also show some other unique characteristics, including higher shearing modulus, higher fracture toughness and excellent absorption properties [17][18][19][20][21]. ...
Article
Artificial architected metamaterials equipped with unique mechanical and physical properties that are naturally inaccessible can be obtained by rational design. In this work, the innovative three-dimensional (3D) chiral and anti-chiral metamaterials are developed referring to the face-rotating polyhedral (FRP) structure present in the virus. Through assembling planar triangular units into the regular octahedron cells, several typical forms of chiral and anti-chiral meta-materials can be obtained by different assembly methods. By changing the topology parameters, the Poisson's ratio can be adjusted between [0, 2.8]. The metamaterials are fabricated by 3D printing utilizing shape memory polymer, and the mechanical properties are analyzed via Finite Element Analysis (FEA) and experiments, including Young's modulus, Poisson's ratio, and tension-twist coupling behavior. In addition, target metamaterial with specific local deformation behavior is obtained by programmatic calculations and distributions to meet special requirements or achieve unique applications. The shape memory property endows the mechanical metamaterials with more potential applications. ARTICLE HISTORY
... This is also reflected in the plethora of results aiming specifically in the control of elastic properties, as they are determined by the stiffness tensor [26][27][28]. The vast majority of the literature focuses in the control of properties such as isotropy, leading to mechanical behavior independent of direction [29][30][31], as well as auxeticity, a property leading to negative Poisson's ratio and resilience to collapse mechanisms such as necking and barrel shape formation [32,33]. ...
Article
Full-text available
Using a new Bayesian Optimization algorithm to guide the design of mechanical metamaterials, we design nonhomogeneous 3D structures possessing the Cauchy symmetry, which dictates the relationship between continuum and atomic deformations. Recent efforts to merge optimization techniques with the design of mechanical metamaterials has resulted in a concentrated effort to tailor their elastic and post elastic properties. Even though these properties of either individual unit cells or homogenized continua can be simulated using multi-physics solvers and well established optimization schemes, they are often computationally expensive and require many design iterations, rendering the validation stage a significant obstacle in the design of new metamaterial designs. This study aims to provide a framework on how to utilize miniscule computational cost to control the elastic properties of metamaterials such that specific symmetries can be accomplished. Using the Cauchy symmetry as a design objective, we engineer structures through the strategic arrangement of 5 different unit cells in a 5 × 5 × 5 cubic symmetric microlattice structure. This lattice design, despite constituting a design space with 5^10 3D lattice configurations, can converge to an effective solution in only 69 function calls as a result of the efficiency of the new Bayesian optimization scheme. To validate the mechanical behavior of the design, the lattice structures were fabricated using multiphoton lithography and mechanically tested, revealing a close correlation between experiments and simulated results in the elastic regime. Ultimately, a similar methodology can be utilized to design metamaterials with other material properties, aspiring to control properties at different length scales, an endeavor that requires inordinate computation cost.
... By means of geometric modeling, Babaee et al. [20] successfully designed a group of metamaterials that can achieve 3D NPR property and theoretically revealed their buckling-induced auxetic effect. And by mimicking the shape of orthogonal truss structure, varied structures have been reported to have 3D NPR effects at specific parameters [21][22][23]. However, in this way, the realization of the 3D auxetic property of the structure appears to be a coincidence without a clear mechanism control strategy. ...
Article
The 3D auxetic buckling pattern in the compression process is used to design auxetic structures. However, obtaining this pattern is time consuming and unintentional. In this paper, three auxetic structures, namely, globally deformed cross-frustum (GC) structure, partially deformed cross-frustum (PC) structure, and core deformed cross-frustum (CC) structure are proposed on the basis of the 3D auxetic deformation equation. The GC structure and PC structure can stably realize the 3D auxetic property through finite element analysis and experimental verification of structures. The structural strength of the latter structure is 2–5 times greater than that of the former structure. The CC structure exhibits a 3D auxetic property during the entire compression process and has excellent structural strength, which is greater than that of the first two structures. The rotational pattern can be also realized by the CC structure within the specified parameter range. A soft crawling robot with a motion module and perception module is designed by using the proposed auxetic structures. The motion module of the soft robot is designed by using the GC structure, and the perception module is realized by using the CC structure. The combination of modules can realize different functions, including advancement and rotation. The robot can be rapidly fabricated by digital light processing and has potential application value in medical treatment and other fields.
... (c) Distributed carbon nanotube sensing concrete [116]. [117]. (b) Two-dimensional lattice structures with negative Poisson's ratio [118]. ...
Chapter
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Recent advances in multifunctional material technologies have paved the way for the creation of innovative multifunctional structures. Exploring multifunctional structures with advanced functionalities is a major step toward a new era of autonomous structural systems for future smart cities. Autonomous structures can respond to their environment, self-monitor their condition, process and store information, and self-program themselves. This chapter presents the state-of-the-art technologies required to build multifunctional material and structures. The central role of structure-dominated, scale-independent architected materials in developing novel types of performance-tailored multifunctional structures is highlighted. We then present a concept toward the next stage of the technological revolution in multifunctional structure science where the so-called engineered self-aware structures can sense, empower, and program themselves using their constituent components. Experimental studies are conducted using composite beam prototypes designed under the proposed concept. We highlight the capabilities of these multifunctional structures to serve as mechanically tunable, self-powered distributed sensing networks with energy harvesting functionally for smart cities infrastructure systems.
... Despite the large number of engineered Poisson's-ratio metamaterial designs, which have been proposed in the last four decades, the field remains rich with new and creative innovations. Some of these innovations include the incorporation of buckling [30][31][32] , origami [33][34][35][36][37] , and kirigami 38,39 to achieve increasingly demanding Poisson's-ratio behaviors. Others have used the random placement of flexible elements 40 , fibers 41,42 , or pores 43 to achieve stochastically engineered negative or zero Poisson's ratio behaviors. ...
Article
Full-text available
Mechanical metamaterials have been designed to achieve custom Poisson’s ratios via the deformation of their microarchitecture. These designs, however, have yet to achieve the capability of exhibiting Poisson’s ratios that alternate by design both temporally and spatially according to deformation. This capability would enable dynamic shape-morphing applications including smart materials that process mechanical information according to multiple time-ordered output signals without requiring active control or power. Herein, both periodic and graded metamaterials are introduced that leverage principles of differential stiffness and self-contact to passively achieve sequential deformations, which manifest as user-specified alternating Poisson’s ratios. An analytical approach is provided with a complementary software tool that enables the design of such materials in two- and three-dimensions. This advance in design capability is due to the fact that the tool computes sequential deformations more than an order of magnitude faster than contemporary finite-element packages. Experiments on macro- and micro-scale designs validate their predicted alternating Poisson’s ratios.
... In the last forty years or so, a variety of methods have been proposed leading to a negative Poisson's ratio. The most prominent methodologies make use of reentrant systems [28][29][30][31][32], involving arrow-shaped ligaments that are pressed in the middle so as to decrease the smaller angle between them; chiral structures [33][34][35][36][37][38][39][40][41][42] in which auxetic behavior is a result of ligament bending and node rotation; rotating rigid or semi-rigid units [43][44][45][46][47], which, as their name implies, achieve this effect through the rotation of units relative to one another; counter rotating units [48][49][50][51] that can harness an internal torque to cause lateral motion; buckling of the material due to elastic instabilities [52][53][54][55][56][57]; and, at a smaller scale, the collective behavior of interacting particles [58][59][60][61][62]. ...
Article
The deformation behavior of intersecting ligaments forming variants of the square and rectangular grids under mechanical compression was investigated. It was shown that such systems are able to exhibit a negative incremental Poisson’s ratio at relatively large axial compressive strains. Numerical simulations and experimental studies indicated that the extent of auxeticity depends on the relative offset of successive ligaments, the relative lengths of the ligaments as well as on their thickness. It was also shown that there are two distinct modes of deformation, one resembling that of the reentrant hexagonal honeycomb and the other that of the meta-tetrachiral system.
... Grima et al. [15,16] proposed a novel perforated plate by cutting randomly which exhibits stable auxetic behavior under tension. Ren and Shen et al [17][18][19][20][21] reported a method of generating auxetic unit cell, and the Poisson's ratio can be adjusted systematically and intuitively using a single factor named pattern scale factor (PSF). However, the auxetic behavior of these structures above is generally addressed by sacrificing the whole stiffness of materials. ...
Article
Full-text available
Auxetic materials have attracted a considerable attention due to their excellent properties, e.g., fracture resistance, shear resistance, energy dissipation, etc. However, the stiffness of auxetics tends to be much weaker than solid structure because of the existence of internal holes. Inspired by tuning the compacted point of auxetic structures to enhance their stiffness, a systematic methodology for defining a single parametric of variable stiffness scale factor (VSF) to generate auxetic unit cell with variable stiffness has been proposed and verified in this study. Two models with different VSF proportions were investigated experimentally. Different centres of rotation, heights of deformation area, and VSF percentages were analyzed to prove the effectiveness of the method numerically. The results indicate that the compacted strain can be tuned effectively using the designed VSF proportions, and the difference between the designed VSF and real VSF could be reduced by slightly changing the height of deformation area. These desirable characteristics provide a new idea for the optimal design of auxetics, with potential application in protective structures.
... Hence, auxeticity has been observed at different scales, from macro-to nano-dimensions. Apart from examples of natural materials with an intrinsic negative Poisson's coefficient [2][3][4][5], auxetic media are generally artificially-made systems, whose microstructure is designed by exploiting different geometries and mechanisms: re-entrant unit cells [6][7][8][9], starshaped inclusions [10,11], chiral configurations [12][13][14][15], double arrowhead honeycombs [16], perforations and cuttings [17][18][19][20][21], rotating rigid units [22], lattices [23][24][25] and elastic instabilities [26,27]. Alternative approaches to design auxetic media are presented in the reviews [28][29][30][31][32]. ...
Article
We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes the medium isotropic in the plane. Remarkably, the mesoscale interaction between the first- and second-level cuts enables the attainment of a value of the Poisson’s ratio close to the minimum reachable limit of -1. The effective properties of the hierarchical auxetic structure are determined numerically, considering both a unit cell with periodic boundary conditions and a finite structure containing a large number of repeating cells. Further, results of the numerical study are validated experimentally on a polymeric specimen with appropriately arranged rank-two cuts, tested under uniaxial tension. We envisage that the proposed hierarchical design can be useful in numerous engineering applications exploiting an extreme auxetic effect.
... With the development of science and technology, high-performance structural materials have become more and more desired in the engineering fields. In this regard, mechanical metamaterials are increasingly popular in the research community [1][2][3][4][5][6][7]. The negative Poisson's ratio (NPR) tube is a typical mechanical metamaterial, which expands (shrinks) transversely under axial compression (tension). ...
Article
Full-text available
The synthesized understanding of the mechanical properties of negative Poisson’s ratio (NPR) convex–concave honeycomb tubes (CCHTs) under quasi-static and dynamic compression loads is of great significance for their multifunctional applications in mechanical, aerospace, aircraft, and biomedical fields. In this paper, the quasi-static and dynamic compression tests of three kinds of 3D-printed NPR convex–concave honeycomb tubes are carried out. The sinusoidal honeycomb wall with equal mass is used to replace the cell wall structure of the conventional square honeycomb tube (CSHT). The influence of geometric morphology on the elastic modulus, peak force, energy absorption, and damage mode of the tube was discussed. The experimental results show that the NPR, peak force, failure mode, and energy absorption of CCHTs can be adjusted by changing the geometric topology of the sinusoidal element. Through the reasonable design of NPR, compared with the equal mass CSHTs, CCHTs could have the comprehensive advantages of relatively high stiffness and strength, enhanced energy absorption, and damage resistance. The results of this paper are expected to be meaningful for the optimization design of tubular structures widely used in mechanical, aerospace, vehicle, biomedical engineering, etc.
... Auxetic metamaterials are typically classified into re-entrant [16][17][18][19][20][21][22][23], chiral [24][25][26][27][28], rotating [29][30][31][32][33][34], and hierarchical laminate structures [35][36][37] according to their deformation mechanisms. In general, the re-entrant, chiral, and rotating structures are porous and composed of a single component, whereas the hierarchical laminate structures are solid and consist of two or more components with different Poisson's ratios. ...
Article
Full-text available
An auxetic metamaterial is a type of mechanical metamaterial that has a negative Poisson's ratio. Most auxetic metamaterials are truss-based or originate from Boolean operations of simple geometries. Herein, we introduce a new 3D auxetic metamaterial that is mathematically generated from an implicit expression. Further, this metamaterial is fabricated by 3D printing using a flexible material, which allows it to recover from large deformations. The buckling-induced auxetic behavior of the metamaterial was first evaluated via compression tests and finite element analyses. A nickel layer was then plated onto the surface to enhance its stiffness, strength, and conductivity without loss of auxeticity and resilience. The integration of 3D printing and electroless plating enabled accurate control over the mechanical and conduction properties of the auxetic metamaterial; these properties are presented as contour maps for guidance in functional applications. We propose a novel 3D auxetic metamaterial derived from a mathematically defined triply periodic minimal surface. The stiffness, strength, and conductivity of the metamaterial are enhanced by nickel plating without loss of auxeticity and resilience. The effective mechanical and conduction properties were mapped against geometric parameters, including relative density and nickel layer thickness. These data maps provide insight for tuning its performance over a broad range.
... Due to these advantages, a series of 3D auxetic metamaterials have been proposed which can be assorted as 3D reentrant honeycomb models [61], 3D double arrow structures [62] and 3D chiral auxetic systems [63][64], etc. Moreover, Wang et al. [65] significantly improved the specific stiffness and strength of three-dimensional double-arrow-head auxetic structures by making them from high-performance fiber-reinforced polymer (FRP) composites, and other researchers have also improved the mechanical properties of 3D negative Poisson's ratio structures through different raw materials such as metals and polymers [61,[66][67][68][69][70][71][72][73], which can further expand the application field of 3D auxetic materials. ...
Article
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As we all know, compression in one direction will cause expansion in the orthogonal direction for conventional materials. Similarly, stretching in one direction will give rise to contraction in the vertical direction. It is hence possible to combine these two properties to obtain a novel mechanism to create 3D structures with negative Poisson’s ratio (PR) in some directions and positive PR in other ones (partial auxetics). The latitude-and-longitude-inspired double-elliptic-ring structures (DERs) with tunable Poisson’s ratio and Young’s modulus are designed and studied in this work, which offers an effective way for achieving this mechanism. A 3D structure with negative Poisson’s ratio in three directions is also obtained via arranging the DERs alternately. Meanwhile, theoretical results show that the magnitude of Poisson’s ratio of DERs can reach -18.3. Experimental and simulation consequences indicate that the DERs can effectively reduce stress concentration and fracture possibility due to its smooth geometry. Another advantage of DERs is that it still has negative Poisson’s ratio effect under large levels of compression. This work can provide a useful reference for the design of 3D auxetic metamaterials with excellent properties, which is promising in some structural and functional applications.
... These include moulding techniques and 3D printing amongst others, both of which have been used to produce a number of auxetic systems including chiral honeycombs, rotating units, and re-entrant systems [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Another method which has risen to the fore in recent years involves the introduction of specific perforation patterns in a conventional or positive Poisson's ratio material [9,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], which results in systems possessing geometries and designs which are similar to those observed in a number of systems with the potential to exhibit auxetic behaviour. This technique has been used thus far to create auxetic perforated systems which resemble rotating unit structures based on squares [49], triangles [50], and cubes [51], amongst others. ...
Article
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Mechanical metamaterials are systems which derive their mechanical properties from their structure rather than their intrinsic material composition. In this work, we investigate a class of highly anisotropic mechanical metamaterials designed by the introduction of diamond and elliptically shaped perforations which possess the ability to show auxetic behaviour. By the use of finite element simulations, we show how these highly tuneable systems have the potential to exhibit a large range of Poisson’s ratios, ranging from highly positive to giant negative values, simply by altering the geometric parameters and orientation of the perforations. The anomalous properties of these systems have also been shown to be retained over significant tensile strain ranges, highlighting the vast potential applicability and functionality of these mechanical metamaterials.
... Compared to their traditional counterparts, mechanical metamaterials have been presented with mechanical advantages and unusual properties such as enhanced deformation resistance [27,29,[38][39][40][41][42][43], enhanced toughness [30,33,[44][45][46][47], ultra-light [35,[48][49][50][51][52], negative mechanical characteristics [18,23,28,[53][54][55][56], well recoverability [25,34,48,49,57], etc. To date, many effective applications of mechanical metamaterials have been reported in the literature [58][59][60][61][62]. including the innovative devices and techniques in energy absorption [63][64][65][66], heat transferring [11,12], microwave [67][68][69][70][71], electromagnetic transducers [72], resonators [73,74], sensors [75,76], and soft robots [77][78][79][80]. ...
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Mechanical metamaterials have opened an exciting venue for control and manipulation of architected structures in recent years. Research in the area of mechanical metamaterials has covered many of their fabrication, mechanism characterisation and application aspects. More recently, however, a paradigm shift has emerged to an exciting research direction towards designing, optimising and characterising mechanical metamaterials using artificial intelligence (AI) techniques. This new line of research aims at addressing the difficulties in mechanical metamaterials (i.e. design, analysis, fabrication and industrial application). This review article discusses the advent and development of mechanical metamaterials, and the future trends of applying AI to obtain smart mechanical metamaterials with programmable mechanical response. We explain why architected materials and structures have prominent advantages, what are the main challenges in the mechanical metamaterial research domain, and how to surpass the limit of mechanical metamaterials via the AI techniques. We finally envision the potential research avenues and emerging trends for using the AI-enabled mechanical metamaterials for future innovations.
... Over these past thirty years, the studies on auxetic materials and structures presented different theoretical and practical aspects. Among others, the search for auxetic properties in new materials [6,7], the theoretical studies of various models exhibiting auxetic properties [8][9][10][11][12][13][14][15][16][17][18][19][20][21], or the creation of auxetic composites in order to enhance mechanical properties of materials [22,23]. The latter is of particular importance if one considers practical applications of negative Poisson's ratio materials [24][25][26][27]. ...
Article
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Limited number of papers describe the practical use of auxetics in the wood and furniture sector. Only one paper describes the auxetic nails. None of them analyzed the impact of using auxetics on the strength of furniture joints. The aim of this investigation was to design and manufacture different kinds of auxetic dowels with corresponding muffs and experimentally, theoretically, and numerically analyze the minimum mounting forces, contact pressures , and friction coefficients of these dowels in particleboard. Firstly, auxetic properties of the dowels were numerically determined, and then obtained values were confirmed by real compression tests in order to be sure that the dowels had negative Poisson's ratios. All dowels were manufactured from polyamide (PA12) with 3D printing Selective Laser Sintering (SLS) technology. Static compression tests were carried out for obtaining the minimum mounting force needed to insert the dowel into the muff. Numerical analyses were performed by means of Abaqus/Explicit v6.14-2 software. Contact pressures and friction coefficients were also theoretically calculated and compared to the results of numerical analyses and real tests. At the end of the tests, the auxetic dowels gave lower mounting force values than the non-auxetic dowels. Mounting force values of dowels decreased as the dowel hole diameter and size of inclusions are increased. Furthermore, the contact pressures on the surface of the auxetic dowels were considerably lower than in the non-auxetic dowels. In conclusion, it could be said that the auxetic dowels could be utilized as an alternative fastener for the traditional furniture dowels. Therefore, withdrawal strength and corner joint tests of the auxetic dowels should be investigated in future studies.
... The 3D extension of the buckling-induced pattern transformation in 2D, also known as "Bucklicrystals" in Figure 12, refers to the periodic arrangement of patterned spherical shells, which undergo isotropic volume reduction in response to a force stimulus, when all ligaments undergo a uniform first buckling mode [71,72]. Further investigations carried out by Shen et al. [73] and Lim et al. [74] proposed the elastomeric NPR structures based on simple initial geometries and the 3D anisotropic intersecting double arrowhead structure respectively. However, Yang et al. reported that for the models they studied, auxetic behavior not only depended on the re-entrant cell shapes, but also depended on the angle. ...
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Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called “designed materials” or “architectured materials” and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson’s ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.
... (H. Li) structure units, which exhibit a series of extraordinary mechanical properties [8]. Mechanical metamaterials with adjustable stiffness, negative compressibility, anti-expansion and bulging performance have been becoming popular in vibration damping devices [9,10]. ...
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Gradually stiffer (GS) mechanical metamaterial is a novel kind of adaptive structures under nonlinear varying loads for cushioning and vibration damping in engineering. These man-made metamaterials in applications are usually tailored by trial-and-error. This study develops a design framework that integrates the topology optimization, parametric design and compression experiment for the GS mechanical metamaterials induced by the negative Poisson's ratio (NPR) property. Firstly, a parametric level set method is incorporated with the numerical homogenization method to topologically optimize a series of microstructural unit cells with different NPRs. Then, the nonlinear static analysis is respectively applied to different unit cells to check their GS behavior. Secondly, typical microstructures with GS property are selected and simplified to perform the subsequent parametric design to analyze the expected property. Thirdly, the obtained mechanical metamaterials are fabricated by using the additive manufacturing (AM). GS properties of the obtained designs are analyzed and verified by both the simulation and compression experiments. Results show that we could obtain the GS mechanical metamaterial based on NPR properties for their similar characteristics. This study demonstrates that the proposed design framework is effective to tailor innovative layouts of the GS mechanical metamaterials.
... In recent years, in order to improve stiffness and strength, auxetic structures have gradually evolved from elastic foam materials to metallic structures. An important characteristic of these metallic structures is that the plasticity of the material is fully utilized to achieve auxetic performance of the structure, since large deformation of metal is commonly developed in the plastic state [36][37][38]. Thus, definition of the Poisson's ratio is also extended from the elastic stage to the plastic one. ...
Article
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Perforated steel plates with regularly shaped holes are already widely employed as steel dampers, which dissipate seismic energy through plastic deformation of steel. As a typical auxetic structure, two-dimensional (2D) re-entrant honeycomb configurations have characteristics of large deformation and good energy absorption. However, research on the effects of these configurations on the mechanical performance of steel is limited. This paper investigated the auxetic properties of perforated steel plates with re-entrant hexagon holes. Repetitive units are controlled by three parameters, hole ratio, re-entrant angle, and chamfer radius. Elastoplastic behavior and damage under large deformation were studied via tension tests and finite element (FE) analysis based on a micromechanics-based ductile fracture model. The effects of different parameters on mechanical properties of configurations were analyzed and discussed. The static performance of the perforated steel plates obtained in this study provides a good basis for its further dynamic study under large deformation.
... Mechanical metamaterials typically possess intricate geometries which are repeated multiple times to form a sheet or block of material. The standard modus operandi used to study these systems takes advantage of this, by employing the use of the representative area or volume elements (RVEs) with periodic boundary conditions to simulate the deformation behaviour of these systems [12][13][14][15][16][17][18][19][20][21][22][23]. This allows one to study stress and strain fields and distributions as well as investigate the mechanical properties of these systems. ...
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The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.
... However, in order to manufacture a 3D auxetic structure, sophisticated processes are required accompanied by different challenges due to technological limitations [8,125]. On the other hand, 2D auxetics can be manufactured through profilerolling of sheet-metal blanks [121], slotting metal sheets [126] or by 3D printing [127][128][129]. Based on the remarks above, the 2D re-entrant topology was implemented in this thesis, due to its relatively-simple geometry, and less expensive fabrication, compared to other auxetic topologies. ...
Thesis
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Blast resistant gates are essential for sensitive infrastructure, such as embassies, ministries or parliaments. Lightweight gates equipped with ‗energy absorbing systems‘ have better operational performance than the traditional costly and bulky design. Graded auxetic structures have not yet been used as potential passive damping systems in the supporting frame of blast resistant gates. Consequently, this thesis tried to design a new graded auxetic damping system and investigate if it could maintain a 3000x4500mm steel gate operable after high blast pressure of , from 100kg TNT at 5m stand-off distance. Blast-induced response of the gate was assessed, with and without the proposed Uniaxial Graded Auxetic Damper (UGAD), using Abaqus/Explicit solver. Results showed that the attachment of the proposed UGAD to the gate, led to a dramatic decrease in permanent deformations (a critical factor for gate operability after a blast event). Hence, a lighter, more economical gate (with 50% reduction in mass) was required to satisfy the operability condition. In addition, 49% of peak reaction forces were diminished, that had a direct impact on the concrete supporting frame. Results also showed that internal energy in the whole model composed mainly of plastic dissipation energy, with 56% achieved from the UGADs, and 44% from the gate. The additional plastic dissipation energy gained from those sacrificial light-weight auxetics justifies the significant reduction in permanent deformations, mass of the gate and reaction forces. Finally, a proper reinforced concrete supporting system was modelled and showed to stay in the elastic range. The UGAD may also be used in different scales for other structural applications, such as; blast-resistant façade and crash energy absorbers in automotive industry. The outcomes of this research may have a positive impact on other sectors beyond academia, such as industry, economy and public safety.
... Characteristic properties for which metamaterials can be designed include negative material indices, force damping, and high massstrength and stiffness. A commonly studied negative index property is Poisson's ratio; these materials are referred to as auxetic metamaterials [6,7]. These can include 3D lattice structures that are designed to collapse or fold in on themselves such as the structures studies by Huang et al. [8] and Schwerdtfeger et al. [9], or 2D perforated sheets such as the bistable auxetic structures studies by Rafsanjani et al. [10]. ...
Article
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Two novel, origami-inspired, metamaterials were designed, mechanically tested, and modelled. One novel origami model was folded using a triangular based crease pattern and the other was folded using a rectangular based crease pattern. The origami-inspired metamaterial sheets were fabricated from polylactic acid using fused deposition additive manufacturing. Several configurations, parameterized by varying the fold angle, were mechanically tested under compression and impact loads. It was found that the specific elastic compression modulus of these novel designs was higher, ranging from 594 MPa/kg to 926 MPa/kg, than existing origami-inspired structures made based on the popular Ron-Resch design, which had specific elastic compression moduli between 15 MPa/kg to 365 MPa/kg. A finite element model further analysed the stress distribution of the core structures under compression loads. The impact testing results showed that the pattern of the tessellated cores affected the amount of impact force transferred through the samples, whereas the fold angle of the origami-inspired design had little impact on the results. The rectangular structure was shown to transfer approximately 50–75% of the force transferred by the triangular structure under impact loads. Keywords: Origami, Metamaterial, Fused deposition modelling, Compression, Impact, Finite element modelling
... However, in order to manufacture a 3D auxetic structure, sophisticated processes are required accompanied by different challenges due to technological limitations [52,56]. On the other hand, 2D auxetics can be manufactured through profile-rolling of sheet-metal blanks [51], slotting metal sheets [57] or by 3D printing [58][59][60]. Based on the remarks above, the 2D re-entrant topology was implemented in this paper, due to its relatively-simple geometry, and less expensive fabrication, compared to other auxetic topologies. ...
Article
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Auxetic structures are efficient cellular materials that can absorb blast/impact energy through plastic deformation, thus protecting the structure. They are developing sacrificial solutions with light weight, high specific strength, high specific toughness and excellent energy dissipating properties, due to its negative Poison's ratio nature. The use of auxetic and non-auxetic panels in blast resistant structures had been relatively perceived by researchers. Nonetheless, implementation of those energy dissipaters, explicitly as a uni-axial passive damper is restrained to limited studies, which highlight the potential need for further explorations. The aim of this paper is the design of a new uniaxial graded auxetic damper (UGAD) that can be used as a blast/impact/shock absorber in different scales for different structural applications. First, the geometry, material, numerical model and loading are introduced. Then, a detailed parametric study is conducted to achieve the most efficient graded auxetic system. Moreover, the designed auxetic damper is numerically tested and its static and dynamic constitutive relations are derived and validated analytically. The selection of optimum parameters was based on the ratio of the reaction force to the applied load (RFd/P) and plastic dissipation energy (PDE). The final designed UGAD contains three auxetic cores that have the same geometry, material grade (6063-T4), size and number of layers equal to eight. The cell-wall thickness t of the three auxetic cores is 1.4 mm, 1.8 mm and 2.2 mm, respectively; composing a graded auxetic system. The performance of the three auxetic cores together have led to a wide plateau region (80% of total crushing strain) and variant strength range (1-10 MPa), which in return, can justify the superior performance of the UGAD under different blast levels. Finally, the 3D printed prototype of the UGAD is presented and the possible applications are covered.
Article
Tissue engineering (TE) scaffolds with appropriate Poisson's ratio (PR) are suitable for mimicking the environment of native tissues on which cells could survive and thrive better. Herein, cellular structured scaffolds are made by a new composite poly(ethylene glycol) diacrylate/cellulose nanofibril aerogel, with prototypes of the hexagonal, reentrant, and semireentrant models. Scaffolds with different geometry parameters (l, t, α) are designed and simulated by COMSOL to enable precise regulation of their PR. Then, nine groups of scaffolds with different PRs ranging from -0.5 to 0.85 are designed by adjusting geometry parameters and fabricated by using stereolithography and freeze-drying techniques. Subsequently, bone marrow mesenchymal stem cells (BMSc) are cultured on these scaffolds for 21 days, during which CCK8 assay, fluorescence microscope observation, and real-time polymerase chain reaction experiments are performed to characterize the proliferation and differentiation of BMSc. The results reflect that the scaffolds with different PR can provide various stress environments for cells, and the scaffold with zero PR is the most suitable for BMSc differentiating into chondrocytes during early culture experiments. This study suggests that tuning PR precisely is an attractive and effective strategy to provide a cells-suitable environment for scaffold fabrication for TE.
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Energy self-sufficiency, as well as optimal management of power in buildings is gaining importance, while obtaining power from traditional fossil energy sources is becoming more and more expensive. In this context, millimeter-scale metasurfaces can be employed to harvest energy from microwave sources. They can also be used as sensors in the microwave regime for efficient power management solutions. In the current study, a simple spray printing method is proposed to develop metasurfaces in construction materials, i.e., plasterboard and wood. Such materials are used in the interior design of buildings; therefore, the implementation of metasurfaces in large areas, such as walls, doors and floors, is realized. The fabricated metasurfaces were characterized regarding their electromagnetic performance. It is hereby shown that the investigated metasurfaces exhibit an efficient electromagnetic response in the frequency range (4–7 GHz), depending on the MS. Thus, spray-printed metasurfaces integrated on construction materials can potentially be used for electromagnetic applications, for buildings’ power self-efficiency and management.
Article
Negative Poisson’s ratio (NPR) structures, also known as auxetics, is attracting growing interests due to their unique mechanical properties and a wide range of potential deployment. More attentions have been paid to explore novel auxetic structures through bionics, lattice cells or origami. However, the systemic design method of NPR structures has not yet mature. Here, a design framework of NPR structures is proposed by integrating freedom, actuation and constraint topologies (FACT) theory and isogeometric analysis. Based on the isogeometric method, the shape and mechanical properties of the curved beam can be changed by adjusting the control points of the curved beam. The configuration library was established by encapsulating curved beams to straight beam. FACT theory is employed to synthesize the cellular structure whose compliant elements are chosen from the curved beam configuration library. In this way, two negative Poisson’s ratio structures were designed. Simulation and experiments demonstrate the feasibility of the proposed design framework of NPR structure. The results of this study have a wide range of potential applications for design future NPR structures. And the work will also provide a new idea to design architected metamaterial systems exhibiting other properties. This article is protected by copyright. All rights reserved.
Chapter
Optimally designed elastomeric cellular structures can safeguard the human body or an engineering system from the blow of an impact as they manifest excellent energy absorption capabilities through undergoing large deformation at constant stress as well as offer high strength to weight ratio. This study aims to develop peculiar lightweight elastomeric cellular structures having high energy-absorbing capabilities that have potential applications in designing reusable energy/shock absorbers. Further, in the present study, we investigate the mechanical properties, deformation, and collapse mechanisms of elastomeric cellular structures with gradually varying pore density throughout the specimen. Results of numerical simulations suggest that structure with non-homogeneous pore density offers better energy absorption capabilities than structures having homogeneous pore density despite overall porosity being similar. Also, the compaction behavior of the structure and the variation in critical stress levels at local instability points can be altered by the gradation of porosity within the structure.KeywordsElastomersPeriodic structureGraded porosityEnergy absorptionMechanical instability
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In this study, the deformation and energy absorption characteristics of a novel hybrid tube is investigated both experimentally and numerically. The architecture of the proposed hybrid tube composed of an inner conventional tube and a co-axially arranged outer auxetic tube. Quasi-static compressive tests were conducted on the auxetic tubes, the conventional tubes and the hybrid tubes. A three-dimensional digital image correlation technique was used to monitor the evolution of radial contraction of the tubes. Measured performance of the tubes were compared in terms of force, energy absorption, and specific energy absorption. Finite element (FE) models were also developed for the three types of tubes, analyzed using ANSYS/LS-DYNA, and validated by experimental measurements. Both experimental and numerical results showed that the presence of the auxetic tube in the hybrid tube alters the deformation mode of the conventional tube by exerting a radial force. Parametric studies were performed to investigate the effects of the outer auxetic tube, wall thickness of the inner conventional tube, the failure strain, and yield strength of the outer tube’s material on mechanical performance of the hybrid tube. Increasing the yield strength of the outer auxetic tube improved both the energy absorption and specific energy absorption characteristics of the hybrid tube significantly.
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We propose the design of a novel three-dimensional porous continuous solid exhibiting negative Poisson’s ratio. The shape and periodic distribution of the pores guarantee cubic symmetry, and the directional dependance of the Poisson’s ratio and Young’s modulus shows a moderate degree of anisotropy and multidirectional auxeticity. We demonstrate the auxeticity of the porous solid numerically, solving both a periodic analysis on a unit cell and a boundary value problem on a finite specimen. The numerical results are fully confirmed by experimental results, obtained from Digital Image Correlation data. The final parametric analysis indicates how to modulate the characteristic parameters of the microstructure in order to tune macroscopic properties. The proposed design maintains a relatively high Young’s modulus and it is prone to large-scale industrial production.
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Nowadays, the development of 3D-printing technology makes it possible for fabricating metamaterials with distinctive mechanical properties. In this paper, we present a novel design of 3D hexa-chiral helical structure with negative Poisson’s ratio and systematically study its mechanical behaviors through experimental, theoretical, and numerical methods. In terms of structural design, besides geometric configurations, we propose a theoretical model to qualitatively analyze the relationship between geometric parameters and structural properties. For actual mechanical properties, an approximate method is presented to decouple the structural deformation based on marks’ displacements. With the assistance of quasi-static compression tests and finite element simulation, the relationship between geometric parameters and elastic mechanical properties is studied. The experimental results are in good agreement with the simulation results. Meanwhile, the special coupled compression-torsion deformation mode is also discussed. Finally, we briefly study the extension effect of the structure in a larger space through numerical simulations. These results are helpful to further optimize the geometric design for customized structural performance to a certain degree.
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For most materials, the sign of Poisson's ratio does not change under tension and compression, i.e., it is positive or negative at the same time. However, this paper reports the design of a novel metamaterial consisting of rods and ropes whose cells have a total of four load-bearing modes. These load-bearing modes will switch with each other upon changing the external loading mode, causing them to exhibit a variety of peculiar properties. For example, a positive Poisson's ratio under tension and a negative Poisson's ratio under compression were achieved along the vertical direction. Secondly, the ratio of the tensile elastic modulus to the compressive elastic modulus of this material could be adjusted over a wide range of 0.1 − 40, which depended on the stiffness of the rope and the angle of the rod. Theoretical and numerical analyses showed that the stiffness matrix of the designed metamaterial was asymmetric, which breaks the classical model in which the stiffness matrix of conventional materials is symmetric. The use of thin rods instead of ropes is also discussed, and a simplified analysis method is given. This material is expected to have applications in many fields, such as wave modulation, biomedical devices, etc.
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Auxetic metamaterials have evolved growing beyond the cellular material structures and offering unique combinations of both auxetic and mechanical properties. However, the understanding and development of these promising material structures have been predominantly based on analytical evaluation methods, as practical implementation was restricted by manufacturing limitations. The manufacturing limitation has changed quite significantly with the advent of additive manufacturing methods, particularly with direct metal printing, such as selective laser melting. Ever since, the auxetic meta material structures began attracting renewed interests, and several different new structural forms and hybridisation of certain existing models followed, focussing specifically on enhancing auxeticity as well as other mechanical attributes. A recently developed and novel S-shaped unit cell based auxetic structure is hybridised with star re-entrant unit cells and analysed both numerically and experimentally based on physical forms produced by selective laser melting as part of the research reported here. Numerical and experimental results correlated sufficiently, depitcing significant enhanced auxeticity as high as −3, and mechanical property with the hybrid structures.
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Materials with an abnormal Poisson’s ratio, including those with negative Poisson’s ratio (NPR) and zero Poisson’s ratio (ZPR), are an important category of mechanical metamaterials, among which many exhibit NPR in all three directions. However, few of them, especially the three‐dimensional (3D) materials, exhibit ZPR in partial directions and NPR in other directions. In this paper, a novel 3D structure developed by orthogonal splicing the two‐dimensional (2D) parallelogram honeycomb structure is proposed. Different from the 2D parallelogram honeycomb with ZPR, the spliced 3D parallelogram structure can exhibit not only ZPR but also NPR in different directions. The analytical model of the structure is established based on the classical beam theory, the equivalent analytical formulas of Young’s modulus and Poisson’s ratio are given, and finite element simulation and experiments are used for verification. The relationship between Young’s modulus and Poisson’s ratio of the structure, as well as its geometric parameters and material parameters, are analyzed using analytical formulas and numerical simulation. The results reveal that the structure is transversely isotropic and can achieve NPR on the transverse symmetry plane and ZPR outside the plane. This unique property may accord this structure with important applications in aerospace, biomedical, and other fields. This article is protected by copyright. All rights reserved.
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Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for ). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D – through the addition of torsional deformation modes and the handling of 3D rotations – results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body’s boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach.
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Auxetic mechanical metamaterials (AMMs), as an exciting paradigm of metamaterials, have attracted increasing attention due to their interesting mechanical properties (e.g. negative Poisson's ratio), as well as emergence of advanced manufacturing technology (e.g. 3D printing). Although various reviews on AMMs: their structures, properties and applications, have existed, it still lacks a comprehensive review in terms of manufacturing methods. In this review, the latest progress in AMMs is extensively reviewed, including AMMs’ structures, characteristics, manufacturing methods and applications. In addition, the current challenges and future works of AMMs are concluded and discussed. This review aims to serve as a collection of knowledge that supplies more comprehensive understanding and inspiration to support further developments of AMMs from the perspective of design and manufacturing. This article is protected by copyright. All rights reserved.
Article
The folded geometry has successfully been transformed into auxetic woven fabric in the literature. However, the influences of the micro‐geometric parameters on the macroscopic behavior have not been addressed yet. In this paper, several key micro‐geometric parameters for the folded geometry were identified and the mechanical behaviors of the folded structure were preliminarily studied by using the finite element method. The results showed that the folded structure can be unfolded in both longitudinal and transverse directions when stretched and thus achieving a negative Poisson's ratio. More interestingly, another fantastic property of tension‐bending coupling effect was found in the folded structure and a competition exists between the auxeticity and the tension‐bending coupling effect. This is the first time to report a structure that can stimulatingly have the auxeticity and the tension‐bending coupling effect. Due to the unique properties, the folded geometry is very promising in some important fields, examples being the textiles, civil engineering and auto industry. The present work may provide a good guide for the design and application of the folded structure. This article is protected by copyright. All rights reserved.
Article
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The design and production of multifunctional materials possessing tailored mechanical properties and specialized characteristics is a major theme in modern materials science, particularly for implementation in high-end applications in the biomedical and electronics industry. In this work, a number of metamaterials with perforated architectures possessing the ability to exhibit a plethora of 2D auxetic responses with negative Poisson's ratios ranging from quasi-zero to large negative values (lower than −3.5), stiffnesses, stretchability and surface coverage properties were manufactured. These systems were produced through the introduction of microstructural cuts in a rubber sheet using direct laser cutting, and analysed using a dual approach involving experimental tests and Finite Element Analysis. In addition to examining the mechanical properties of the perforated metamaterials, the influence of edge effects and material thickness on the deformation behaviour of these systems were investigated, with re-entrant systems shown to possess anomalous deformation profiles which are heavily dominated by the boundary regions. These findings highlight the effectiveness of this method for the fabrication of auxetic metamaterial sheets as well as the large variety of mechanical properties, deformation mechanisms and load responses which may be obtained through what may be effectively described as simply the introduction of patterned cuts in a thin sheet.
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This paper details a new 2D auxetic honeycomb that was structured by mirroring the horizontal series-connected parallelograms along the vertical direction. A combination of analytical, numerical, and experimental methods was used to gain a deep understanding of the elastic behavior of the new honeycomb and examined its dependence on the geometric parameters. The results showed that the new honeycomb can achieve a negative Poisson's ratio via a novel mechanism. Furthermore, the newly developed 2D honeycomb was extended to three dimensions, and three kinds of 3D structures were conceived via different splicing methods. A preliminary numerical study was conducted to explore the mechanical properties of the 3D structures. An auxetic effect was found in two principal orthogonal coordinate directions of those 3D structures when they were compressed along the other principal axis. This work may provide a new insight into the design of both the 2D and 3D auxetics.
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Auxetic polymeric materials are a special kind of materials that exhibit negative Poisson’s ratio (NPR)effect. They get fatter when stretched and thinner when compressed. Auxetic behavior is a scale-independent property which can be achieved at different structural levels from molecular tomacroscopic levels. The internal structure of material plays an important role in obtaining auxeticeffect. Because of NPR effect, auxetic polymeric materials demonstrate a series of particularcharacteristics when compared with conventional materials. In recent years, a variety of auxeticpolymeric materials have been designed and fabricated for diverse applications. This article presents areview on advances in this area. The emphasis is focused on the geometrical structures and models,particular properties and applications of auxetic polymeric materials developed.
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Mechanical properties of materials have long been one of the most fundamental and studied areas of materials science for a myriad of applications. Recently, mechanical metamaterials have been shown to possess extraordinary effective properties, such as negative dynamic modulus and/or density, phononic bandgaps, superior thermoelectric properties, and high specific energy absorption. To obtain such materials on appropriate length scales to enable novel mechanical devices, it is often necessary to effectively design and fabricate micro-/nano- structured materials. In this Review, various aspects of the micro-/nano-structured materials as mechanical metamaterials, potential tools for their multidimensional fabrication, and selected methods for their structural and performance characterization are described, as well as some prospects for the future developments in this exciting and emerging field.
Article
Auxetics are a modern class of material that, unlike conventional materials demonstrate a lateral expansion when longitudinally loaded due to a negative Poisson's ratio (v). One novel way of introducing repeatability into the auxetic process is through the employment of three dimensional (3D) printing technologies in an additive manufacturing technique. Through implementing these technologies, any random cell orientation is removed, as idealized auxetic foam topologies can be digitally designed, simulated, and finally printed from a wide range of materials, including pliable polymers. Auxetic microstructure can also be obtained through the scanning of conventional auxetic foam structures using computed tomography (CT), and then replicated as models as demonstrated by Baker in the production of auxetic spinal implants.
Article
Auxetics are a modern class of material fabricated by altering the material microstructure. Unlike conventional materials, auxetics exhibit a negative Poisson's ratio when subjected to tensile loading. These materials have gained popularity within the research community because of their enhanced properties, such as density, stiffness, fracture toughness and dampening. This paper provides a critical oversight of the auxetic field with particular emphasis to the auxetic foams, due to their low price, easy availability and desirable mechanical properties. Key areas discussed include the fabrication method, the effects played by different parameters (temperature, heating time, cell shape and size and volumetric compression ratio), microstructural models, mechanical properties and potential applications.
Article
The results of an experimental investigation into pattern switching phenomena in three-dimensional cellular structures under compression are reported. It is found that the switch is mediated above a critical strain by an elastic instability which is coupled throughout the structure. Surprisingly, the phenomena are found to be essentially two-dimensional in nature with a uniform pattern switch in one of the directions orthogonal to the applied uniform strain. Selection of the direction of the pattern switch is realized using biaxial loading and the results interpreted in terms of multiple bifurcations. The relevance of the results to the construction of ordered 3D cellular structures and their use in phononic and photonic devices is discussed.
Article
Buckling is exploited to design a new class of three dimensional metamaterials with negative Poisson's ratio. A library of auxetic building blocks is identified and procedures are defined to guide their selection and assembly. The auxetic properties of these materials are demonstrated both through experiments and finite element simulations and exhibit excellent qualitative and quantitative agreement.
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
In this work we show that a structure consisting of a network of bending beams can exhibit a negative Poisson’s ratio. We have shown that the negative Poisson’s ratio behaviour is driven by the (bcc analogous) type III beams, the type II (fcc like) beams result in a structure with a Poisson’s ratio of around zero and type I (simple cubic configuration) beams result in a Poisson’s ratio of nearly +1. The tensile and shear strengths of the type III beams are augmented by addition of type II and type III beams. By tailoring the relative stiffness of the component beams within the structure it is possible to design an auxetic truss structure with specific Poisson’s ratio, tensile and shear moduli.This validates the hypothesis that crystal structures can provide inspiration for macro structures with tailored mechanical properties where the mechanism for negative Poisson’s ratio (auxetic) behaviour at the atomic scale in cubic crystals is replicated by bending beams.
Article
Recently, novel and uniform deformation-induced pattern transformations have been found in periodic elastomeric cellular solids upon reaching a critical value of applied load [Mullin, T., Deschanel, S., Bertoldi, K., Boyce, M.C., 2007. Pattern transformation triggered by deformation. Phys. Rev. Lett. 99, 084301; Boyce, M.C., Prange, S.M., Bertoldi, K., Deschanel, S., Mullin, T., 2008. Mechanics of periodic elastomeric structures. In: Boukamel, Laiarinandrasana, Meo, Verron (Eds.), Constitutive Models for Rubber, vol. V. Taylor & Francis Group, London, pp. 3–7]. Here, the mechanics of the deformation behavior of several periodically patterned two-dimensional elastomeric sheets are investigated experimentally and through numerical simulation. Square and oblique lattices of circular voids and rectangular lattices of elliptical voids are studied. The numerical results clearly show the mechanism of the pattern switch for each microstructure to be a form of local elastic instability, giving reversible and repeatable transformation events as confirmed by experiments. Post-deformation transformation is observed to accentuate the new pattern and is found to be elastic and to occur at nearly constant stress, resulting in a superelastic behavior. The deformation-induced transformations have been physically realized on structures constructed at the millimeter length scale. This behavior should also persist at the micro and nano length scales, providing opportunities for transformative photonic and phononic crystals which can switch in a controlled manner and also exploiting the phenomenon to imprint complex patterns.
Article
Poisson's ratio is, for specified directions, the ratio of a lateral contraction to the longitudinal extension during the stretching of a material. Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, this property is generally believed to be rare in crystalline solids. In contrast to this belief, 69% of the cubic elemental metals have a negative Poisson's ratio when stretched along the [110] direction. For these metals, we find that correlations exist between the work function and the external values of Poisson's ratio for this stretch direction, which we explain using a simple electron-gas model. Moreover, these negative Poisson's ratios permit the existence, in the orthogonal lateral direction, of positive Poisson's ratios up to the stability limit of 2 for cubic crystals. Such metals having negative Poisson's ratios may find application as electrodes that amplify the response of piezo-electric sensors.
Article
The paper presents the first scientific study of the stiffness, strength and energy absorption characteristics of the luffa sponge with a view to using it as an alternative sustainable engineering material for various practical applications. A series of compression tests on luffa sponge columns have been carried out. The stress-strain curves show a near constant plateau stress over a long strain range, which is ideal for energy absorption applications. It is found that the luffa sponge material exhibits remarkable stiffness, strength and energy absorption capacities that are comparable to those of some metallic cellular materials in a similar density range. Empirical formulae have been developed for stiffness, strength, densification strain and specific energy absorption at the macroscopic level. A comparative study shows that the luffa sponge material outperforms a variety of traditional engineering materials.
Article
Auxetics are novel counterintuitive materials that grow thicker perpendicularly to the applied force when stretched and therefore are described by a negative Poisson's ratio. We show that a regular lattice of individual multipods properly assembled in three dimensions has the ultimate negative Poisson's ratio −1: the lattice expands or contracts uniformly in all directions. Our ball-and-stick working model verifies the mathematical construction. Application of the model to real materials is discussed. Our result is important for understanding the ways to create entangled materials with interesting mechanical properties.
Article
The ubiquity of multifunctional cellular solids in both natural and engineered materials is a clear indication of the importance of such materials. The mechanical behavior of these structures is the most common critical functionality across different applications. In this Communication, we establish the effective elastic properties of periodic bicontinuous solid/air structures that can be fabricated at small length scales by interference lithography and compare their properties with standard models.
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Soft cellular structures that comprise a solid matrix with a square array of holes open avenues for the design of novel soft and foldable structures. Our results demonstrate that by simply changing the shape of the holes the response of porous structure can be easily tuned and soft structures with optimal compaction can be designed.
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Dip-in direct-laser-writing (DLW) optical lithography allows fabricating complex three-dimensional microstructures without the height restrictions of regular DLW. Bow-tie elements assembled into mechanical metamaterials with positive/zero/negative Poisson's ratio and with sufficient overall size for direct mechanical characterization aim at demonstrating the new possibilities with respect to rationally designed effective materials.
Article
An extensive experimental database has been established for the structural behaviour of aluminium foam and aluminium foam-based components (foam-filled extrusions). The database is divided into three levels, these are: (1) foam material calibration tests, (2) foam material validation tests and finally (3) structural interaction tests where the foam interacts with aluminium extrusions. This division makes it possible to validate constitutive models applicable to aluminium foam for a wide spectrum of loading configurations. Several existing material models for aluminium foam from the literature are discussed and compared. To illustrate the use of the database, four existing material models for foams in the explicit, non-linear finite element code LS-DYNA have been calibrated and evaluated against configurations in the database.
Article
Zhao-Qing Zhang and colleagues describe a new elastic metamaterial that can behave like an elastic solid or a fluid depending on the frequency and direction of propagation. The key to their discovery is the design of a complex building block that is a practical realization of a system of four coupled masses and springs. In their approach, this unit cell consists of four rectangular steel rods that are arranged around a central hard silicone rod and contained inside a larger soft silicone rod, with the entire unit embedded in a soft foam matrix. When these units are arranged in a simple square lattice, this two-dimensional system has a quite wide range of frequencies in which the effective dynamic mass density is negative owing to a dipolar resonance of the four steel rods. The second negative band allows only longitudinal waves to propagate along one of the principal directions of the crystal and only shear waves in the other principal direction, leading to a material with a fluid-solid mixed behavior.
Article
Negative Poisson's ratio behavior has been uncovered in cellular solids that comprise a solid matrix with a square array of circular voids. The simplicity of the fabrication implies robust behavior which is relevant over a range of scales. The behavior results from an elastic instability which induces a pattern transformation and excellent quantitative agreement is found between calculation and experiment.
Article
Responsive behavior, which is intrinsic to natural systems, is becoming a key requirement for advanced artificial materials and devices, presenting a substantial scientific and engineering challenge. We designed dynamic actuation systems by integrating high-aspect-ratio silicon nanocolumns, either free-standing or substrate-attached, with a hydrogel layer. The nanocolumns were put in motion by the "muscle" of the hydrogel, which swells or contracts depending on the humidity level. This actuation resulted in a fast reversible reorientation of the nanocolumns from tilted to perpendicular to the surface. By further controlling the stress field in the hydrogel, the formation of a variety of elaborate reversibly actuated micropatterns was demonstrated. The mechanics of the actuation process have been assessed. Dynamic control over the movement and orientation of surface nanofeatures at the micron and submicron scales may have exciting applications in actuators, microfluidics, or responsive materials.
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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