Microscopic Buckling Analysis of Cellular Solids Based on a Homogenization Theory of Finite Deformation

基于有限变形均匀化理论的多孔固体微观屈曲分析

基本信息

批准号：
13650084
负责人：
OHNO Nobutada
金额：
$ 2.69万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

The microscopic symmetric bifurcation buckling of cellular solids subjected to macroscopically uniform compression was studied. To begin with, describing the principle of virtual work for infinite periodic materials in the updated Lagrangian form, we built a homogenization theory of finite deformation, which satisfies the principle of material objectivity. Then, we stated a postulate that at the onset of microscopic symmetric bifurcation, microscopic velocity becomes spontaneous, yet changing the sign of such spontaneous velocity has no influence on the variation in macroscopic states. By applying the postulate to the homogenization theory, we derived the conditions to be satisfied at the onset of microscopic symmetric bifurcation. The homogenization theory and buckling conditions established were employed to analyze the in-plane biaxial buckling of an elastic hexagonal honeycomb. We thus found the following : Simple, double and triple bifurcations can take place, if the largest compressive load is transmitted in one, two and three directions of cell walls, respectively. At the double and triple bifurcation points, uniaxial buckling modes develop simultaneously in the two and three directions of cell walls and are linearly combined to generate a biaxial mode, Mode II, reported by Gibson and Ashby (1997) and a flower-like mode, Mode III, observed by Papka and Kyriakides (1999a). In other words, these biaxial modes result from the multiplicity of bifurcation, so that they have very complex cell-patterns in comparison with the uniaxial buckling mode, Mode I, occurring at the simple bifurcation points. Moreover, we showed that Modes II and III, as well as Mode I, are classified as microscopic symmetric bifurcation in spite of their very complex cell-patterns, since they are not macroscopically influenced by changing the sign of spontaneous perturbed velocity as described in the postulate.

研究了经受宏观均匀压缩的细胞固体的微观对称分叉屈曲。首先，以更新的拉格朗日形式描述无限周期性材料的虚拟工作原理，我们建立了有限变形的均质化理论，该理论满足了材料客观性的原理。然后，我们指出，在微观对称分叉开始时，微观速度变得自发，但是改变这种自发速度的迹象对宏观状态的变化没有影响。通过将假设应用于同质化理论，我们得出了在微观对称分叉开始时要满足的条件。建立的均质理论和屈曲条件被用来分析弹性六边形蜂窝的平面双轴屈曲。因此，我们发现了以下内容：如果分别以一个，两个和三个方向传输最大的压缩负荷，则可以进行简单，双重和三分叉。在双分叉点上，单轴屈曲模式同时在细胞壁的两个和三个方向上同时发展，并线性合并以生成双轴模式，Mode II，Gibson和Ashby（1997）报道，由Papka和Kyriakides（19999999999）观察到了花朵样模式，模式III。换句话说，这些双轴模式是由于分叉的多样性而产生的，因此与单轴屈曲模式（模式I）相比，它们具有非常复杂的细胞模式，该模式是在简单的分叉点出现的。此外，我们表明模式II和III以及模式I和模式I被归类为微观对称分叉，尽管它们具有非常复杂的细胞图案，因为这些细胞模式并未受到宏观影响的影响。