Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials
Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials
复制标题
各向异性弹性超材料的多位移微结构连续体建模
DOI：
10.1016/j.wavemoti.2011.12.006
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发表时间：
2012-04-01
期刊：
影响因子：
2.4
通讯作者：
Huang, G. L.
中科院分区：
文献类型：
--
作者：
Liu, A. P.;Zhu, R.;Huang, G. L.
考虑了一种由环氧树脂基体中涂有椭圆橡胶的铅圆柱体制成的弹性超材料，并对其各向异性的有效动态质量密度张量进行了数值计算和论证。为了同时捕捉复合材料中的偶极共振运动和微结构变形，提出了一种新的多位移微结构连续体模型。在公式中，额外的位移和运动学变量被引入来描述全局和局部变形，分别。通过简化的方法推导了二维各向异性弹性异向介质的宏观控制方程。为了验证电流模型，波频散曲线从电流模型进行了比较，从纵向和横向波的有限元模拟。在声波和光波模式中观察到非常好的一致性。本文的工作可为含非基元微结构的弹性异向材料的连续介质建模提供一个基准。(C)2011 Elsevier B.V.保留所有权利。
An elastic metamaterial made of lead cylinders coated with elliptical rubbers in an epoxy matrix is considered, and its anisotropic effective dynamic mass density tensor is numerically determined and demonstrated. To capture both dipolar resonant motion and microstructure deformation in the composite, a new multi-displacement microstructure continuum model is proposed. In the formulation, additional displacement and kinematic variables are introduced to describe global and local deformations, respectively. The macroscopic governing equations of the two-dimensional anisotropic elastic metamaterial are explicitly derived through a simplified procedure. To verify the current model, wave dispersion curves from the current model are compared with those from the finite element simulation for both longitudinal and transverse waves. Very good agreement is observed in both the acoustic and optic wave modes. This work could provide a benchmark of continuum modeling of elastic metamaterials with nonelementary microstructures. (C) 2011 Elsevier B.V. All rights reserved.