非均匀材料损伤破坏的多尺度耦合理论(固体力学).doc

A multi-scale coupling theory for damage and failure of heterogeneous materials ZHANG Tian-jun, XU Hong-jie, LI Shu-gang, REN Shu-Xin （1 College of Sciences, Xian University of Science and Technology; Xian 710054,China；2 College of Energy, Xi’an University of Science and Technology, Xi’an 710054, ChinaAbstract: In order to study the impact of micro-damage on the macro-failure of heterogeneous materials, we built a 3-D micro-element strength distribution model for heterogeneous materials. On the basis of the average field model and the group sharing model, and in accordance with the simulation results, an adjacent element weight sharing model was built. We used the microscopic statistical method to establish the probability function and the trans-scale sensitivity function of macroscopic failure caused by microscopic damage. The study result shows that (1) the larger the damage fraction and the nominal stress of the materials are, and the closer the distance between the damage group is, the greater the macroscopic damage probability is; (2) when the damage fraction is smaller, the material’s trans-scale sensitivity increases with the increase of damage fraction; (3) when damage fraction is larger, the material’s trans-scale sensitivity decreases as the damage fraction increases; and (4) the material’s trans-scale sensitivity is dependent on the size of the system, and the larger the system, the smaller the sensitivity.Key word: multi-scale; strength distribution; damage probability; sensitivity 非均匀材料损伤破坏的多尺度耦合理论? , 许鸿杰1, 李树刚2，任树鑫1 (1西安科技大学 理学院，陕西 西安 710054西安科技大学 学院，陕西 西安 710054) 为研究微损伤对非均匀材料宏观破坏的影响，建立了三维微单元强度分布模型，在平均场模型和集团分担模型的基础上，根据模拟计算结果建立了邻近单元加权分担模型；采用细观统计的方法建立了微观损伤造成宏观破坏的概率函数及跨尺度敏感性函数。结果表明：材料的损伤分数和名义应力越大，破坏集团之间的距离越近，宏观破坏概率就越大；损伤分数较小时，材料的跨尺度敏感性随损伤分数增加而增大；损伤分数较大时，材料的跨尺度敏感性随损伤分数增加而减小；材料的跨尺度敏感性 关键词:多尺度；强度分布；破坏概率；敏感性 中图分类号：O34 文献标识码：A0引言 时空尺度是客观世界的基本特征，例如湍流的涡、固体材料的损伤破坏都涉及大小不同的尺度；同时尺度也是人类认识客观世界的手段和展开科学活动的方法，例如天文学涉及的时空尺度多为光年，微生物学涉及的时空尺度是分米和微米。为了对客观世界中诸如材料的失效、地震或