Double‐Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson's Ratio Properties

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Intuitively, materials become both shorter and wider when compressed along their length.Here we show how a composite material or structure can display a simultaneous reversal in the direction of deformation for both the axial and transverse dimensions, corresponding to negative values of effective stiffness and effective Poisson's ratio, respectively. A negative Poisson's ratio [1] (NPR or auxetic [2] ) host assembly stabilising (otherwise unstable) embedded negative stiffness [3] [4,5] Metamaterials include negative refractive index [6] and negative effective mass density [7] materials finding use in, for example, electromagnetic and acoustic cloaking/lensing applications, respectively. Examples of mechanical metamaterials are negative compressibility transition, [4] NPR [1] and NS [3] materials.Auxetic materials and structures exist, and are stable in the unconstrained state, at the nanoscale (e.g. crystalline forms of silica, [8] zeolites [9] and cellulose [10] ), microscale (microporous polymers [11] and microfabricated truss-like structures [12] ) and macroscale (composite laminates, [13] foams, [14,15] honeycombs [16] and patterned elastomeric spherical shells [17] ). Enhanced shear modulus, [18] energy absorption [19] and indentation resistance [20] are some of the benefits known for auxetic materials and structures. [21] Periodic arrangements of sub-units leading to auxetic behaviour include truss, [16,22] corner-sharing polygon, [23,24] and hybrid truss-polygon [25] frameworks, and particle assemblies. [26,27] NS materials and structures, on the other hand, are thermodynamically unstable unless stabilised by an external constraint.[28] Examples of NS materials include polymethacrylimide (PMI) foams, [16] honeycombs and lattices, [29,AA1,AA2] and certain crystals (VO 2 , BaTiO 3 )undergoing constrained phase transformation. [30,31] The NS effect can also be displayed by constrained buckled tube [32] , buckled beam [33] or multiple magnet [34] systems. Whereas our system is demonstrated to display NS under quasi-static loading, it should be pointed out that a number of these previous studies [3,[30][31][32] measured the dynamic modulus. Dynamic loading of NS materials can give rise to beneficial temporary effects demonstrated, for example, in 3 3 composite systems containing NS inclusions or elements which display extreme stiffness [30] and vibration damping [3,32] responses.Our 'double-negative' mechanical metamaterial displaying simultaneous negative Poisson's ratio and negative stiffness properties comprises an auxetic host framework constraining embedded NS elements. The framework consists of a regular array of interlocked rigid hexagonal sub-units with 3 male and 3 female keys per sub-unit, arranged in an alternating fashion around the six sides of the hexagon [27] (Figure 1...

Pneumatic elastostatics of multi-functional inflatable lattices: realization of extreme specific stiffness with active modulation and deployability

“…Artificially engineered materials can achieve a wide range of tailor-made multi-functional abilities which may not always be available in naturally occurring materials [1][2][3][4][5]. Their micro-scale design can present unprecedented and unconventional, yet useful, properties like ultra-lightweight characteristics [6][7][8][9], shape programming [6,10], crushing resistance and high specific energy absorption [11][12][13][14], auxetic properties [15][16][17][18][19], negative elastic moduli [20][21][22], meta-fluid characteristics [23,24], negative mass density [25,26], tunable wave propagation characteristics and vibration control [27][28][29], programmable constitutive laws [30][31][32], active mechanical property modulation [33][34][35][36][37] and many other multiphysical properties [38][39][40][41][42]. The use of such metamaterials in structural systems can result in the most optimal use of materials along with fulfilling multiple other structural demands simultaneously.…”

Tunable integrated quasi-zero-stiffness metamaterials for ultra-low-frequency vibration isolation

“…The development of metamaterial in recent years has provided us with ideas for realizing special properties of structures [18][19][20]. Various forms of metamaterial have been widely used in the fields of vibration control [21][22][23][24][25][26], shock isolation [27], energy absorption [28][29][30][31] and equivalent parameter [32][33][34]. Some metamaterial with negative-stiffness characteristic provide idea for designing new positive-negative parallel QZS element [35][36][37][38][39].…”

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“…In addition, the miniaturization of mechanical metamaterials can greatly improve the impact/energy absorption per unit mass. A common strategy is to use magnetic inclusions in the system to achieve structural stiffness control [18][19][20]. Hamzehei et al [21] analyzed a new type of bionic friction mechanical metamaterial with zero Poisson's ratio from both macro and micro aspects, and carried out 3D printing and research at the micro level, showing good energy absorption and dissipation properties.…”