Improved designs of negative Poisson’s ratio structure and their applications in aerospace engineering

doi:10.11949/0438-1157.20240878

Abstract

Abstract:

Lightweight have become the development requirements of aircraft structure design and manufacturing in the field of aerospace. The lightweight and porous structure and excellent mechanical properties of negative Poisson’s ratio materials are new carriers to meet this demand. This review covers the types and deformation mechanisms of negative Poisson’s ratio materials, discusses the improved structures of the negative Poisson’s ratio materials and their properties in different dimensions, and summarizes the application prospects in the aerospace field. Also, the challenges and opportunities of the negative Poisson’s ratio materials for future research are proposed.

Key words: negative Poisson’s ratio, design, mechanical properties, numerical simulation, aerospace

摘要：

轻量化和多功能性已成为航空航天领域飞行器结构设计和制造的发展需求，负泊松比材料轻质多孔的结构形式和优异的力学性能，是满足这一需求的新载体。本文从负泊松比结构的种类和变形机理角度出发，重点论述了不同维度下改进设计后负泊松比材料的结构特点及其性能的变化，同时讨论了负泊松比材料在航空航天领域的应用前景，最后对负泊松比结构在未来发展中可能遇到的挑战和机遇进行了总结和展望。

关键词: 负泊松比, 设计, 力学性能, 数值模拟, 航空航天

CLC Number:

TB 301

Shengyi ZHUANG, Chengwei LI, Wenchao XIANG, Junbo XU, Chao YANG. Improved designs of negative Poisson’s ratio structure and their applications in aerospace engineering[J]. CIESC Journal, 2024, 75(11): 3951-3972.

庄晟逸, 李成伟, 向文超, 徐俊波, 杨超. 负泊松比结构的改进设计及其在航空航天中的应用[J]. 化工学报, 2024, 75(11): 3951-3972.

Figures/Tables 14

Fig.1 Schematic diagrams of positive/negative Poisson’s ratio materials under tension/compression (transparent blocks represent the initial state)

Fig.2 Classification of NPR structures(a1)—(a4) re-entrant type: re-entrant hexagon[16], double arrow-shaped[17], petal[18], and star-shaped structures[19]; (b1)—(b4) chiral type: trichiral, tetrachiral, anti-tetrachiral, and hexachiral structures[20]; (c1)—(c4) rotating rigid body: rotating triangles, rotating squares, rotating rectangles[21], and other rotating structures[22]; (d1)—(d4) perforate: I shaped slits, straight slits[23], elliptical holes[24], and other shape holes[25]

Table 1 Deformation patterns of representative auxetic unit cells and their analytical expressions of Poisson’s ratio

内凹六边形

$ν_{12} = - \frac{l s i n θ c o s θ}{g - l s i n θ} [\frac{\frac{l^{2}}{t^{2}} - 1 + \frac{12 (1 + ν_{s})}{5}}{\frac{l^{2} c o s^{2} θ}{t^{2} s i n θ} + s i n θ + \frac{12 (1 + ν_{s}) c o s^{2} θ}{5}}]$

ν_s:母材泊松比；t:胞元壁宽;θ:内凹角;

g:水平支撑柱长度；l:斜支撑柱长度

[26]

六手性

$ν = \frac{4 {(\frac{t}{l})}^{2}}{{(\frac{t}{l})}^{4} c o s^{2} β + 1 - c o s^{2} β + 3 {(\frac{t}{l})}^{2}} - 1$

l: 韧带长度; t: 韧带厚度；β：韧带与径向夹角

[27]

旋转矩形刚体

$ν_{12} = \frac{a^{2} s i n^{2} (\frac{θ}{2}) - b^{2} c o s^{2} (\frac{θ}{2})}{a^{2} c o s^{2} (\frac{θ}{2}) - b^{2} s i n^{2} (\frac{θ}{2})}$

a, b: 旋转刚体边长; θ:旋转刚体夹角

[28]

穿孔板

—

[25]

Table 1 Deformation patterns of representative auxetic unit cells and their analytical expressions of Poisson’s ratio

胞元类型

变形模式

泊松比解析式

文献

内凹六边形

ν_s:母材泊松比；t:胞元壁宽;θ:内凹角;

g:水平支撑柱长度；l:斜支撑柱长度

[26]

六手性

$ν = \frac{4 {(\frac{t}{l})}^{2}}{{(\frac{t}{l})}^{4} c o s^{2} β + 1 - c o s^{2} β + 3 {(\frac{t}{l})}^{2}} - 1$

l: 韧带长度; t: 韧带厚度；β：韧带与径向夹角

[27]

旋转矩形刚体

$ν_{12} = \frac{a^{2} s i n^{2} (\frac{θ}{2}) - b^{2} c o s^{2} (\frac{θ}{2})}{a^{2} c o s^{2} (\frac{θ}{2}) - b^{2} s i n^{2} (\frac{θ}{2})}$

a, b: 旋转刚体边长; θ:旋转刚体夹角

[28]

穿孔板

—

[25]

Fig.3 3D NPR structures(a1)—(a4) cubic lattices: (a1), (a2) re-entrant hexagon cubic lattice[40-43], (a3) chiral cubic lattice[44], and (a4) rotating solid[45]; (b1)—(b5) tubular structures: (b1) re-entrant structure, (b2) anti-trichiral structure[46], (b3) orthogonal elliptical holes[47], (b4) peanut-shaped holes[48], and (b5) rotating rectangle rigid tubular structure[49]; (c1)—(c3) other structures: (c1) chiral dodecahedron lattice[50], (c2) hexagonal perforated honeycomb[51], and (c3) star-shaped tubular structure[52]

Fig.4 Reinforced design of re-entrant unit cells(a) horizontal and vertical strut[72]; (b) wedge-shaped parts[77]; (c) combined walls[74]; (d) comparison of the increasing rate of elastic modulus and relative Poisson's ratio

Fig.5 (a) Embedded hierarchical honeycomb[82]; (b) Vertex-based hierarchical honeycomb[85]; (c) 2-order anti-tetrachiral metastructure[90]; (d) Comparison of the increasing rate of elastic modulus and relative Poisson’s ratio

Fig.6 (a) Russian doll-type deployable cubes based on origami units[91]; (b) Stent based on a two-level hierarchical rotating square geometry[92]; (c) 3D auxetic hierarchical crash box model[93]

Fig.7 Graded re-entrant structures(a) thickness-graded[104]; (b) size-graded[99]; (c) deformation patterns of the angle-graded and uniform structures with the increase of compressive strain[105]

Fig.8 (a) Perforation cells with different gradient distributions and their tensile strain models[55]; (b) Graded mechanical metamaterials with three substructures and their tensile deformation[110]; (c) Comparison between the actual deformation and the target strain functions of the shape-matching metamaterials[111]

Fig. 9 (a) Optimal layout and dilation of the 2D nonuniform vascular stent[112]； (b) Experimental and FEA images of a cylindrical shell made of network materials under axial compression, as-fabricated and under tension[113]； (c) Soft bending actuator with asymmetric metamaterials and its deformed states under different pressures[114]

Fig.10 (a) Curved beams are used instead of the inclined beams to form cosine re-entrant structures[116]； (b) Geometric design of re-entrant double-arrow hybrid honeycomb[117]； (c) Schematics of graded re-entrant circular auxetic honeycombs[107]； (d) A level-3 hierarchical structure with synchronized deformation[89]

Fig.11 (a) Tape springs applied in satellite[121]； (b) The model of re-entrant tape spring[122]； (c) Reflector with elliptic voids and the displacement distribution [125]

Fig.12 (a) Airfoil profile with different cellular configurations[127, 131]; (b) The structure of morphing wing after deformation[128]; (c) Schematic diagram of variable area wing structure[129]; (d) Morphing wing skins with various lattice structures [130]

Fig.13 (a) Distribution of different homogenized cellular configurations for the gradient core[14]； (b) Fuselage section with NPR structure inserts below the cargo floor[137]

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