Elastoplastic microscopic bifurcation and post-bifurcation behavior of periodic cellular solids
Elastoplastic microscopic bifurcation and post-bifurcation behavior of periodic cellular solids
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DOI：
10.1016/j.jmps.2003.07.002
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发表时间：
2004-03
影响因子：
5.3
通讯作者：
D. Okumura;N. Ohno;H. Noguchi
中科院分区：
文献类型：
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作者：
D. Okumura;N. Ohno;H. Noguchi
在这项研究中，一个通用的框架来分析微观分叉和分叉后行为的弹塑性，周期性的细胞固体。该框架是建立在一个双尺度理论的基础上，称为均匀化理论，更新的拉格朗日类型。由此导出了微观分岔的本征模问题和本征模所满足的正交性。正交性允许宏观增量独立于本征模态，从而导致基于比较固体概念的弹塑性分叉后分析的简单过程。利用该框架，对面内压缩弹塑性蜂窝结构的胞元集合体进行了分叉和分叉后分析。因此，演示一个基本的，长波的本征模式的微观单轴压缩下的分叉，它示出的本征模式的纵向分量占主导地位的横向分量，从而导致微观屈曲本地化在一个细胞行垂直于加载轴。研究结果进一步表明，在等双轴压缩作用下，宏观稳定状态下的花状屈曲模式由于宏观不稳定状态下的六重分叉而转变为非对称的长波模式，导致三角洲区域的微观屈曲局部化.
In this study, a general framework is developed to analyze microscopic bifurcation and post-bifurcation behavior of elastoplastic, periodic cellular solids. The framework is built on the basis of a two-scale theory, called a homogenization theory, of the updated Lagrangian type. We thus derive the eigenmode problem of microscopic bifurcation and the orthogonality to be satisfied by the eigenmodes. The orthogonality allows the macroscopic increments to be independent of the eigenmodes, resulting in a simple procedure of the elastoplastic post-bifurcation analysis based on the notion of comparison solids. By use of this framework, then, bifurcation and post-bifurcation analysis are performed for cell aggregates of an elastoplastic honeycomb subject to in-plane compression. Thus, demonstrating a basic, long-wave eigenmode of microscopic bifurcation under uniaxial compression, it is shown that the eigenmode has the longitudinal component dominant to the transverse component and consequently causes microscopic buckling to localize in a cell row perpendicular to the loading axis. It is further shown that under equi-biaxial compression, the flower-like buckling mode having occurred in a macroscopically stable state changes into an asymmetric, long-wave mode due to the sextuple bifurcation in a macroscopically unstable state, leading to the localization of microscopic buckling in deltaic areas.