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周期性细胞固体的微观分叉和生成后行为。该框架是基于更新的Lagrangian类型的两尺度理论（称为均化理论）建立的。因此得出了特征分叉的本本特征问题和特征模式所满足的正交性。结果表明，正交性允许宏观的增量独立于征本征素模，从而简单地进行了基于比较固体通知的固体通知，通过使用上述框架的框架，对比较固体的通知进行了简单的步骤，并通过上述框架进行了分析，并在分析后表现出了蜂巢的分析，以期为蜂巢的蜂巢表现出蜂蜜的蜂巢蜂巢。压缩。这证明了在单轴压缩下的微观分叉的基本的，长波的本征模，因此表明本亚元素具有纵向成分的主导性……更偏向横向成分，因此导致显微镜屈曲在垂直于载荷轴的细胞行中定位在细胞行中。进一步表明，在宏观稳定状态下发生的类似花样的屈曲模式在宏观不稳定状态下的分解分叉导致的不对称，长波模式变为不对称的长波模式，从而导致微观屈曲的位置和短暂的蜂蜜屈曲。使用两尺度理论分析双轴压缩。通过将细胞骨料作为周期单位，分析分叉和分娩后行为，以讨论屈曲应激对周期性长度的依赖性。结果表明，随着周期长度的增加，屈曲应力会降低，并且如果周期性长度足够长，则在宏观不稳定性发作后发生很长的屈曲。然后，通过根据两尺度分析来探索宏观不稳定性条件来得出一个简单的公式，以评估平面双轴压缩下的非常长的屈曲应力。使用能量方法验证了所得公式。较少的