中文摘要：

Gibson公式由于形式简单而被广泛应用,然而,随着六边形蜂窝材料相对密度和变形程度的增大,Gibson公式将逐渐失效。笔者通过有限元数值模拟,对不同相对密度（细长比）等壁厚正六边形蜂窝材料进行分析。定义了非线性修正因子,由数值结果可知,对于低密度蜂窝结构,非线性因子只与变形程度有关,而与密度本身无关。为此,给出了低密度蜂窝非线性修正因子的一个简便拟合式,得到了低密度蜂窝结构几何非线性本构关系。为了将该本构推广到高密度,引入了另一个非线性修正因子,并给出该非线性因子关于细长比和应变的三次多项式拟合结果,从而建立适用于应变和密度在较大变化范围的等壁厚正六边形蜂窝材料弹性大变形本构关系。该本构参数少、精度高、适用范围广,便于工程应用。此方法还可方便地推广到更一般的六边形蜂窝材料。

英文摘要：

Gibson＇s formula is widely used due to its simplicity.Yet,it will lose its effectiveness gradually with the increase of relative density（or the ratio of cell-wall thickness t to length L,t/L）and deformation of hexagonal honeycombs.In this paper,the right hexagonal honeycombs with uniform cells but in different densities were analyzed via finite element analysis.A nonlinear modified factor was introduced here to describe the geometric nonlinear behavior of honeycombs.It can be concluded from the numerical results that,for low density honeycombs,the nonlinear modified factor only relates to the deformation and doesn＇t relate to density.Then,a constitutive relation for low density honeycombs was obtained by giving a fitting formula to the modified factor.For extending this result to high density honeycombs,another nonlinear modified factor was introduced.This modified factor is dependent on both density and deformation.Similarly,a cubic polynomial was used to fit it.Consequently,the geometrical nonlinear constitutive relation which suitable to various density right hexagonal honeycombs with uniform cells wasobtained.The constitutive relation with less parameters and accurate prediction may be promising in applications.And the method used in this paper can be easily extended to general hexagonal honeycomb materials.