基于均匀化理论的混凝土宏细观力学特性研究  

Study on concrete in macro-and meso-scale mechanical properties based on homogenization theory

作　　者：唐欣薇[1] 张楚汉[1] 

机构地区：[1]清华大学水利水电工程系水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《计算力学学报》2009年第6期876-881,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(90510018)资助项目

摘　　要：在细观层次上将混凝土视为由砂浆基质、骨料及其界面组成的三相复合材料，在此基础上，采用有限元方法，对混凝土弹性本构关系进行数值模拟，利用位移渐近展开技术和均匀化理论建立了多尺度力学框架下的有限元平衡方程，重点考察了单胞尺寸对宏观力学性能的影响，得到了相对最大骨料粒径的最小单胞尺寸，即5～10倍最大骨料粒径。作为例证，对混凝土三点弯梁进行了宏细观尺度数值仿真研究，结果表明：基于本文方法可以较好地反映混凝土的宏观力学行为。此外，由于骨料、砂浆的相互作用，应力分布呈现出宏观渐变平滑与细观局部突变的特征。In this paper, concrete is taken as a type of three-component composite material composed of mortar matrix, aggregates and interfaces on the meso-scale. Based on the homogenization theory and finite element method, the equivalent macro-elastic constitutive relationship of concrete is analyzed. Through the use of asymptotic expansion of the displacement and the homogenization theory, the FEM equilibrium equations in multi-scale are established. In this analysis, the influence of unit cell size on the elastic properties in macro-scale is studied and the minimum ratio of unit cell size to the maximum aggregate diameter has been obtained, i.e. 5-10 times of the maximum aggregate diameter. Finally, comparison analysis of the macroscopic and the mesoscopic simulation of a 3-Point concrete beam are presented. It is concluded that the macroscopic characteristics of the concrete can be predicted with good accuracy by the presented method. It is also observed that the stress distribution appears a gradual and smooth variation on the macro-scale while a local abrupt change on the meso-scale due to the interaction between mortar matrix and aggregates.

关 键 词：混凝土 细观力学 均匀化理论 渐近展开 随机骨料模型 

分 类 号：TU37[建筑科学—结构工程]