An Unusual 3D Metamaterial with Zero Poisson's Ratio in Partial Directions

Abstract

As an important material parameter, Poisson's ratio is defined as the negative of the ratio of transverse strain and longitudinal strain under uniaxial compression (tension). In general, Poisson's ratios of materials are positive, that is, a material contracts (expands) in the directions transverse to the direction of stretching (compression). For example, Poisson's ratio of metal is about 0.3 and Poisson's ratio of rubber is 0.5. In addition to positive Poisson's ratio (PPR), some materials have unusual Poisson's ratios, including negative Poisson's ratio (NPR) and zero Poisson's ratio (ZPR).NPR materials are also regarded as auxetic materials, as they contract (expand) in the transverse direction under uniaxial compression (tension). [1] Examples of natural materials with NPR are iron pyrite monocrystals [2] and some cubic elemental metals. [3] In 1987, Lakes [4] constructed the first man-made NPR materials from polyurethane foam, and various NPR materials were subsequently designed. Current NPR structures mainly include chiral structures, [5][6][7] re-entrant structures, [8][9][10] and rotating element structures. [11,12] Cabras proposed a class of isotropic cubic lattice structure with an omnidirectional NPR. [13] NPR structures exhibit multiple superior properties compared with ordinary materials, such as improved shear resistance, [14] fracture resistance, [15] indentation resistance, [16] and energy absorption properties. [17] Therefore, NPR structures have been extensively applied in biomedicine, [18] textile materials, [19] protective tools, [20] intelligent sensors, [21] and other fields.For ZPR materials, the lateral dimension remains constant under an axial strain (stretching or compressing). For PPR and NPR structures, restrained Poisson's contraction (or bulging) occurs in the nonmorphing direction, resulting in a substantial increase in the effective modulus in the morphing direction. However, the unique properties of ZPR structures prevent this issue, [22,23] resulting in incomparable application advantages in biological tissue, [24] deformed wing, and other fields. Therefore, many ZPR structures have been proposed, including SILICOMB, [25] a semi re-entrant honeycomb (SRH), [26] a hybrid cellular honeycomb, [22] a chevron honeycomb and its alternative configuration, and an accordion-like honeycomb. [27] Some novel ZPR structures have recently been developed, and include the hexagon-plate combined structure, [28] the four-pointed star configuration, [23] and the mixed cruciform honeycomb. [29] However, the studies on materials with ZPR have primarily focused on 2D situations.Regarding studies on 3D ZPR structures, Wang et al. [30] extended three 2D ZPR honeycombs (semi re-entrant [SRE] and reversed semi re-entrant [RSRE] and hybrid forms of SRE and RSRE) to 3D honeycombs, and the 3D SRE and 3D hybrid honeycombs can simultaneously achieve an in-plane NPR effect and out-of-plane ZPR effect. Kamran et al. [31] reported a SRE

Geometric nonlinear analysis of dielectric layer based on concave paper-cut structure with zero Poisson’s ratio

“…The linear equivalent Poisson's ratio has almost no change with the increase of strain, and the analytical solution of the nonlinear Poisson's ratio has an obvious downward trend as strain increases. Although Poisson's ratio will change with strain [59][60][61][62], it is near zero, and the change is relatively small. The structure still belongs to zero Poisson's ratio structure.…”

On the effect of the poisson’s ratio on samples subjected to shearing

“…The corpus of knowledge on auxetics has expanded significantly in the last decades [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], particularly since the manufacture of the first soft auxetic material-a foam-which could be easily stretched and compressed by hand [23]. These novel materials were attributed several enhanced characteristics which are not normally manifested by their conventional counter-parts [24][25][26][27][28][29][30][31], which made them particularly appealing to the sports community [32][33][34][35][36][37][38].…”

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“…Honeycomb structures have been widely studied in the fields of aerospace, automobile, and navigation owing to their excellent properties including high specific stiffness and strength, low volume consumable ratio, excellent fatigue stability, impact resistance and thermal insulation [1][2]. And it commonly includes regular hexagons, concave hexagons, rhombus, regular quadrilateral, circle, star, arrow, etc.…”