基于均匀化方法的多孔材料细观力学特性数值研究

本文把均匀化理论与有限元法相结合 ,应用于多孔材料的弹性本构数值模拟 ,利用位移渐进展开建立了均匀化有限元列式。通过对正方形孔洞蜂窝材料有效模量的计算比较 ,表明本文方法可得到较准确的有效模量 ;同时还考察了胞壁固体相的力学性能参数vs 对宏观力学性能的影响 ,得到了与一些理论公式相同的结论。最后 ,本文对胞壁中含有弹性增强相的多孔材料的力学性能进行了数值研究 ,并利用二次均匀化方法给出定量的计算结果

Microscopic Investigation of Cellular Materials Mechanical Properties Based on Homogenization Theory

The finite element method is combined with homogenization theory based on asymptotic expansion for predicting the macro and microscopic properties of cellular materials. Through the use of asymptotic expansion of the displacement, the control equations of periodic micro|structure are established and the homogenization FEM for analyzing two|dimensional periodic materials is developed. By comparing the results of present method with those of other methods, we can see that Homo FEM can give more accurate results of effective modulus. At the same time, we analyze the influence of poiss ratio of solid phase on the macro|mechanical properties of cellular materials and give the same result as some experiential formulae. Further, by appliying the methods of designing composite materials, we can add elastic inclusions with greater modulus in cell wall to derive more elastic cellular materials without affecting the void ratio, for which this paper gives quantitative analysis and results.