Large-scale Multiscale Analysis for Microscopic Buckling and Macroscopic Instability of Periodic Cellular Solids Based on a Homogenization Theory

基于均质化理论的周期性多孔固体微观屈曲和宏观不稳定性的大规模多尺度分析

基本信息

批准号：
15360051
负责人：
OHNO Nobutada
金额：
$ 6.46万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15360051/
关键词：
Homogenization Theory Cellular solid Microscopic buckling Macroscopic instability Multiscale analysis Honeycomb

项目摘要

In this study, first, a general framework was developed to analyze microscopic bifurcation and post-bifurcation behavior of periodic cellular solids. The framework was built on the basis of a two-scale theory, called a homogenization theory, of the updated Lagrangian type. The eigenmode problem of microscopic bifurcation and the orthogonality to be satisfied by the eigenmodes were thus derived. It was shown that 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.Second, by use of the framework mentioned above, bifurcation and post-bifurcation analysis were performed for cell aggregates of an elastoplastic hexagonal honeycomb subject to in-plane compression. Thus, demonstrating a basic, long-wave eigenmode of microscopic bifurcation under uniaxial compression, it was shown that the eigenmode has the longitudinal component dominant … More to the transverse component and consequently causes microscopic buckling to localize in a cell row perpendicular to the loading axis. It was 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.Third, long-wave and short-wave buckling of elastic square honeycombs subject to in-plane biaxial compression were analyzed using the two-scale theory. By taking cell aggregates to be periodic units, the bifurcation and post-bifurcation behavior were analyzed to discuss the dependence of buckling stress on periodic length. It was shown that buckling stress decreases as periodic length increases, and that very-long-wave buckling occurs just after the onset of macroscopic instability if the periodic length is sufficiently long. Then, a simple formula to evaluate the very-long-wave buckling stress under in-plane biaxial compression was derived by exploring the macroscopic instability condition in the light of the two-scale analysis. The resulting formula was verified using an energy method. Less

在这项研究中，首先，开发了一个一般框架来分析分叉和生物后行为的牢房，该框架是基于更新的Lagangian类型的两个规模理论（称为同质化理论）建立的。分叉和对本征模的正交性被施加了，这使得某些性质允许本征素模的宏观递增，从而基于比较固体概念的弹性塑性分析的简单过程。 By the Framework Mentalk Mented Above, Bifurcation And Post-Bifurcation Analysis Were PERFORMED FORLL AGGRR Egates of An Elastoplastic Hexagonal Honeycomb Subject to In-Plane Compression. Thus, Demonstrating a Basic, Long-Wave Eigenmode of Microscopic Bifurcation Under UNIAXIAL COMPRESSION ONENT AND CAUSES MICROSCOPIC屈曲至垂直于载荷轴的细胞行，在宏观上屈曲的花状屈曲变为不对称的，长波模式的torcation torcat torcat torcat ion三角洲区域。使用理论理论分析了弹性方形蜂窝的三分，长波和短波屈曲，以期为周期性。周期性的压力显示，屈曲条纹应力设计为驴，如果周期性的长度足够长，则很长的巨型波脉络。应力应力，使用能量方法验证了所得公式