Homogenization and equivalent in-plane properties of two-dimensional periodic lattices

被引:169
|
作者
Gonella, Stefano [1 ]
Ruzzene, Massimo [1 ]
机构
[1] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA
关键词
homogenization; hexagonal lattices; auxetic materials; wave propagation;
D O I
10.1016/j.ijsolstr.2008.01.002
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The equivalent in-plane properties for hexagonal and re-entrant (auxetic) lattices are investigated through the analysis of partial differential equations associated with their homogenized continuum models. The adopted homogenization technique interprets the discrete lattice equations according to a finite differences formalism, and it is applied in conjunction with the finite element description of the lattice unit cell. It therefore allows handling of structures with different levels of complexity and internal geometry within a general and compact framework, which can be easily implemented. The estimation of the mechanical properties is carried out through a comparison between the derived differential equations and appropriate elasticity models. Equivalent Young's moduli, Poisson's ratios and relative density are estimated and compared with analytical formulae available in the literature. In-plane wave propagation characteristics of honeycombs are also investigated to evaluate phase velocity variation in terms of frequency and direction of propagation. Comparisons are performed with the values obtained through the application of Bloch theorem for two-dimensional periodic structures, to show the accuracy of the technique and highlight limitations introduced by the long wavelength approximation associated with the homogenization technique. (c) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2897 / 2915
页数:19
相关论文
共 50 条
  • [31] Homogenization of a sandwich structure and validity of the corresponding two-dimensional equivalent model
    Saidi, A
    Coorevits, P
    Guessasma, M
    JOURNAL OF SANDWICH STRUCTURES & MATERIALS, 2005, 7 (01) : 7 - 30
  • [32] Contact process in disordered and periodic binary two-dimensional lattices
    Fallert, S. V.
    Kim, Y. M.
    Neugebauer, C. J.
    Taraskin, S. N.
    PHYSICAL REVIEW E, 2008, 78 (04):
  • [33] Resonant Zener tunneling in two-dimensional periodic photonic lattices
    Desyatnikov, Anton S.
    Kivshar, Yuri S.
    Shchesnovich, Valery S.
    Cavalcanti, Solange B.
    Hickmann, Jandir M.
    OPTICS LETTERS, 2007, 32 (04) : 325 - 327
  • [34] Symmetric interactions of plane solitons in two-dimensional nonlinear lattices
    Nikitenkova, Svetlana
    Stepanyants, Yury
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 114
  • [35] Wave Propagation Feature in Two-Dimensional Periodic Beam Lattices with Local Resonance by Numerical Method and Analytical Homogenization Approach
    Zhou, C. W.
    Sun, X. K.
    Laine, P.
    Ichchou, M. N.
    Zine, A.
    Hans, S.
    Boutin, C.
    INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2018, 10 (04)
  • [36] Boosting in-plane anisotropy by periodic phase engineering in two-dimensional VO2 single crystals
    Ran, Meng
    Zhao, Chao
    Xu, Xiang
    Kong, Xiao
    Lee, Younghee
    Cui, Wenjun
    Hu, Zhi-Yi
    Roxas, Alexander
    Luo, Zhengtang
    Li, Huiqiao
    Ding, Feng
    Gan, Lin
    Zhai, Tianyou
    FUNDAMENTAL RESEARCH, 2022, 2 (03): : 456 - 461
  • [37] Substrate effects on the in-plane ferroelectric polarization of two-dimensional SnTe
    Fu, Zhaoming
    Liu, Meng
    Yang, Zongxian
    PHYSICAL REVIEW B, 2019, 99 (20)
  • [38] Stabilization of the in-plane vortex state in two-dimensional circular nanorings
    Mamica, S. (mamica@amu.edu.pl), 1600, American Institute of Physics Inc. (113):
  • [39] In-plane Hall effect in two-dimensional helical electron systems
    Zyuzin, Vladimir A.
    PHYSICAL REVIEW B, 2020, 102 (24)
  • [40] Theory of the in-plane photoelectric effect in two-dimensional electron systems
    Mikhailov, S. A.
    Michailow, W.
    Beere, H. E.
    Ritchie, D. A.
    PHYSICAL REVIEW B, 2022, 106 (07)