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.

研究了宏观均匀压缩下多孔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材料的虚功原理，建立了满足材料客观性原理的有限变形均质化理论。然后，我们提出了一个假设，即在微观对称分岔开始时，微观速度变得自发，但改变这种自发速度的符号对宏观状态的变化没有影响。通过将该假设应用于均质化理论，我们推导了微观对称分岔开始时需要满足的条件。利用所建立的均质化理论和屈曲条件，对弹性六边形蜂窝体的面内双轴屈曲进行了分析。因此，我们发现：如果最大的压缩载荷分别沿细胞壁的一个、两个和三个方向传递，则可能会发生简单分叉、双重分叉和三重分叉。在双分叉点和三分叉点，单轴屈曲模式在细胞壁的两个和三个方向上同时发展，并线性组合生成双轴模式，模式 II，由 Gibson 和 Ashby (1997) 报道，以及花状模式，模式 III，由 Papka 和 Kyriakides (1999a) 观察到。换句话说，这些双轴模式是由多重分叉产生的，因此与发生在简单分叉点的单轴屈曲模式（模式 I）相比，它们具有非常复杂的单元模式。此外，我们表明，尽管模式 II 和 III 以及模式 I 具有非常复杂的单元模式，但它们仍被归类为微观对称分岔，因为它们在宏观上不受改变自发扰动速度符号的影响，如假定。