With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever before.This paper is focused on the prediction methods of effective Young's modulus for periodical cellular materials.Based on comprehensive studies of the existing homogenization method(HM),the G-A meso-mechanics method(G-A MMM) and the stretching energy method(SEM) that are unable to reflect the size effect,we propose the bending energy method(BEM) for the first time,and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM method.Meanwhile,the underlying characteristics of each method and their relations are clarified.To do this,the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four methods.Stretch and bending models of periodical cellular materials are taken into account,respectively for the comparison of stretch and flexural displacements resulting from the above methods.We conclude that the BEM has the strong ability of both predicting the effective Young's modulus and revealing the size effect.Such a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal cell.On the contrary,other three methods can only predict the limited results whenever the cell size tends to be infinitely small.
随着航空航天与民用技术对多孔材料应用的广泛需求,对于该种轻质材料的研究达到了空前的高度.该文着重研究了周期性多孔材料等效杨氏模量的有效计算方法,在综合分析现有均匀化方法、G-A(Gibson and Ashby)细观力学方法、拉伸能量法无法反映体胞尺寸效应的基础上,提出了弯曲能量新方法,并对4种方法的预测效果进行了系统的研究,揭示了弯曲能量法的通用性、尺寸效应的预测能力以及与4种方法的内在联系与差异.以拉伸和弯曲两种力学加载模型的有限元数值计算结果以及文献给出的六边形蜂窝实测实验结果为基准,比较分析了4种方法在预测拉伸变形和弯曲挠度的计算精度.结果表明,弯曲能量法能很好地预测不同构型蜂窝单胞的等效杨氏模量及其尺寸效应,并能很好反映不同加载模式下结构变形随多孔材料体胞尺寸的变化规律包括六边形蜂窝的非单调变化趋势,而其他3种方法仅能预测体胞无限小时的极限结果.
