颗粒增强复合材料弹性结构的双尺度有限元分析  

Two Scale Analysis of Elastic Structures of Particle Reinforced Composite Materials with Finite Element Method

作　　者：杨晓东[1] 董泽民[1] 杨坤[1] 申长雨[1] 

机构地区：[1]郑州大学橡塑模具国家工程研究中心,郑州450002

出　　处：《机械工程学报》2012年第8期34-38,共5页Journal of Mechanical Engineering

基　　金：国家自然科学基金(10872186);河南省教育厅自然科学计划(2010A130002)资助项目

摘　　要：颗粒增强方法是实现材料高性能化的重要手段。预测颗粒增强复合材料的细观结构与力学性能的关系是实现材料增强增韧的基础。为更好地分析、设计和优化复合材料,需要引入多尺度计算模型来考察细观结构对宏观力学性能的影响。基于均匀化理论,采用Voronoi有限元法对颗粒增强复合材料进行细观数值模拟,从而预测材料的宏观等效弹性常数,并直接得到材料的细观应力场。在细观尺度,首先假设满足平衡条件的应力场,采用Voronoi应力单元建立余能泛函并得到细观控制方程,最终形成可直接求解的线性代数方程组,从而求得应力系数并得到细观应力场。在宏观尺度,利用商业有限元软件ANSYS来进行宏观结构分析。通过均匀化方法求得弹性模量的宏观平均值,将其输入ANSYS系统即可进行计算,由此把宏细观两个尺度耦合起来,可以对颗粒增强复合材料构成的结构体进行有效的力学分析。Particle reinforcement method is an important measure to improve the properties of materials.To predict the relationships among micro structures and mechanical properties of a composite material is a basis to realize stronger of materials.It is favorable to introduce multi-scale models in order to investigate the influence of micro structures on macro mechanical properties for better analysis,design and optimation of composite materials.Based on homogenization theory,using Voronoi cell finite element method to perform numerical simulation to particle reinforced composite materials.The macro equivalent elastic constants of a composite material can be predicted,and the micro stress fields are attained directly.In micro scale,the equilibrated stress fields are first assumed,and Voronoi stress cells are adopted to get the complimentary energy functional,so that the control equations can be established,and a set of linear algebraic equations that can be directly resolved is formed.Finally,the stress coefficients are calculated and the micro stress fields are attained.In macro scale,the macro structure analysis is done with the finite element analysis software ANSYS.The macro average value of elastic module is calculated by homogenization method,which is inputed into the ANSYS system to perform calculations.So that the two scales of macro and micro can be coupled and a mechanical analysis can be executed to the structures made of particle reinforced composite materials.

关 键 词：复合材料 弹性变形 细观力学 有限元法 

分 类 号：TP304[自动化与计算机技术—计算机系统结构] TB125[自动化与计算机技术—计算机科学与技术]