中文摘要：

在分析炭黑填充橡胶复合材料的宏观与细观特征之间联系的基础上，提出了具有随机分布形态的代表性体积单元，推导并应用了周期性细观结构的边界约束条件，建立了三维多颗粒夹杂代表性体积单元的数值模型，对炭黑填充橡胶复合材料的宏观力学行为进行了模拟仿真。研究表明，该模型通过周期性边界条件的约束保证了宏观结构变形场和应力场的协调性；计算得到的炭黑填充橡胶复合材料的弹性模量明显高于未填充橡胶材料，并随着炭黑颗粒所占体积分数的增加而增大；该模型对复合材料有效弹性模量的预测结果与实验结果吻合较好，而且比Bergstrom三维模型的预测结果更好，证实了该模型能够用于炭黑颗粒增强橡胶基复合材料有效性能的模拟分析。

英文摘要：

Based on the relation of macroscopic and microscopic characteristics of carbon black filled rubber composites, representative volume element with random distribution pattern has been proposed, the boundary conditions for the periodic microstructures has been discussed, and three dimensional multi-particles RVE numerical model has been established to study and analyze the macro mechanical properties of the carbon black filled rubber composites by the micromechanical finite element method. The research shows that the compatibility of the deformation field and stress field in macrostructure are ensured by the periodic boundary conditions, the modulus of the rubber composite is increased considerably with the introduction of carbon black filler particles, and the effective elastic modulus of the rubber composite is increased with the increase of the carbon black particle volume fraction. In the simultaneous, the results of the prediction on the effective elastic modulus of the rubber composite made with this numerical model are consistent with the experimental results, and better than the predictions of the model proposed by Bergstrom, which demonstrate that this model can be used for simulation analysis of effective properties of the carbon black filler particle reinforced rubber matrix composites.