Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach

被引:292
作者
Mousanezhad, Davood [1 ]
Haghpanah, Babak [1 ]
Ghosh, Ranajay [1 ]
Hamouda, Abdel Magid [2 ]
Nayeb-Hashemi, Hamid [1 ]
Vaziri, Ashkan [1 ]
机构
[1] Northeastern Univ, Dept Mech & Ind Engn, Boston, MA 02215 USA
[2] Qatar Univ, Mech & Ind Engn Dept, Doha, Qatar
关键词
Chiral; Hierarchical; Honeycomb; Metamaterial; Auxetic;
D O I
10.1016/j.taml.2016.02.004
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The effects of two geometric refinement strategies widespread in natural structures, chirality and self-similar hierarchy, on the in-plane elastic response of two-dimensional honeycombs were studied systematically. Simple closed-form expressions were derived for the elastic moduli of several chiral, anti-chiral, and hierarchical honeycombs with hexagon and square based networks. Finite element analysis was employed to validate the analytical estimates of the elastic moduli. The results were also compared with the numerical and experimental data available in the literature. We found that introducing a hierarchical refinement increases the Young's modulus of hexagon based honeycombs while decreases their shear modulus. For square based honeycombs, hierarchy increases the shear modulus while decreasing their Young's modulus. Introducing chirality was shown to always decrease the Young's modulus and Poisson's ratio of the structure. However, chirality remains the only route to auxeticity. In particular, we found that anti-tetra-chiral structures were capable of simultaneously exhibiting anisotropy, auxeticity, and remarkably low shear modulus as the magnitude of the chirality of the unit cell increases. (C) 2016 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.
引用
收藏
页码:81 / 96
页数:16
相关论文
共 76 条
[1]   Skeleton of Euplectella sp.:: Structural hierarchy from the nanoscale to the macroscale [J].
Aizenberg, J ;
Weaver, JC ;
Thanawala, MS ;
Sundar, VC ;
Morse, DE ;
Fratzl, P .
SCIENCE, 2005, 309 (5732) :275-278
[2]   Hierarchical honeycombs with tailorable properties [J].
Ajdari, Amin ;
Jahromi, Babak Haghpanah ;
Papadopoulos, Jim ;
Nayeb-Hashemi, Hamid ;
Vaziri, Ashkan .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2012, 49 (11-12) :1413-1419
[3]   The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs [J].
Alderson, A. ;
Alderson, K. L. ;
Chirima, G. ;
Ravirala, N. ;
Zied, K. M. .
COMPOSITES SCIENCE AND TECHNOLOGY, 2010, 70 (07) :1034-1041
[4]   Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading [J].
Alderson, A. ;
Alderson, K. L. ;
Attard, D. ;
Evans, K. E. ;
Gatt, R. ;
Grima, J. N. ;
Miller, W. ;
Ravirala, N. ;
Smith, C. W. ;
Zied, K. .
COMPOSITES SCIENCE AND TECHNOLOGY, 2010, 70 (07) :1042-1048
[5]  
[Anonymous], 1997, CELLULAR SOLIDS STRU
[6]   Homogenization of periodic hexa- and tetrachiral cellular solids [J].
Bacigalupo, Andrea ;
Gambarotta, Luigi .
COMPOSITE STRUCTURES, 2014, 116 :461-476
[7]   An experimental investigation of deformation and fracture of nacre-mother of pearl [J].
Barthelat, F. ;
Espinosa, H. D. .
EXPERIMENTAL MECHANICS, 2007, 47 (03) :311-324
[8]  
Boresi A., 2003, ADV MECH MAT
[9]  
Bornengo D, 2005, P I MECH ENG G-J AER, V219, P185, DOI [10.1243/095441005X30216, 10.1243/095441005x30216]
[10]   Design and Fabrication of a Passive 1D Morphing Aircraft Skin [J].
Bubert, Edward A. ;
Woods, Benjamin K. S. ;
Lee, Keejoo ;
Kothera, Curt S. ;
Wereley, N. M. .
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, 2010, 21 (17) :1699-1717