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中文摘要：
结合均匀化理论与不动点迭代法，提出了均匀化方法用于解决周期性多尺度问题的有限元框架，建立了具有典型微观结构的TiC颗粒增强钛基复合材料的单胞有限元模型．从宏观尺度出发采用不动点迭代方法给出了微观尺度下单胞有限元的位移边界条件，对其拉伸力学性能进行了数值模拟研究．给出了TiC颗粒增强钛基复合材料在拉伸载荷作用下的宏观等效力学性能，并与实验结果进行对比，验证了该方法的有效性和可靠性．
英文摘要：
Finite element （FE） framework for solving the periodic multi-scale problems is presented by using homogenization theory and fixed point iteration method. FE unit cell models of TiC particle reinforced titanium matrix composites with typical micro-structure were established. Displacement boundary conditions for FE cell models were obtained from macro- scale by adopting the fixed point iteration method. Numerical simulations were performed to study the tensile behaviors of the TiC particle reinforced titanium matrix composites and the macro-effective mechanical properties were given. A good agreement is achieved between the experimental results and the numerical predictions, revealing the reliability and effectiveness of the presented techniques.
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