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中文摘要：
具有周期性胞元的超轻质材料在制造和应用过程中，不可避免地会出现基体材料、微结构拓扑和尺寸的随机性变化.此时，评价材料的等效弹性性能需要借助基于均匀化方法（周期性边界条件）或代表体元法（周期性边界条件，均匀应力或均匀应变边界条件等）的蒙特卡洛模拟.该文首先通过算例分析和比较了不同边界条件下的数值结果，讨论了结果的尺度效应和对胞元选取的依赖性.为了提高和改善Dirichlet边界条件下的计算效率和结果，提出了一种考虑内部胞元能量等效的代表体元法.该方法能够有效削弱边界条件和胞元选取的影响，从而实现了采用较小的代表体元得到更好的结果.数值算例验证了方法在预测确定性材料和随机性材料等效模量时的有效性.
英文摘要：
When ultra-light materials with periodic micro-structures are manufactured and applied in engineering, there always exist stochastic variations in matrix materials, topology and size of microstructures, etc. One way to evaluate elastic properties of materials with imperfections is to use Monte Carlo simulation based on homogenization theory （with periodic boundary） or representative volume element method （with periodic boundary, uniform stress boundary or uniform strain boundary）. In the first section of this paper, effective modules of ultra-light materials with imperfections are evaluated and compared under different types of boundary conditions. In this way, the influences of different boundary conditions on the predictions are discussed in detail, and the dependence of results on the size and topology of the RVE selected for computation is discussed as well. To improve the efficiency of computation and refine the results under Dirichlet boundary condition, a representative volume element computation based on energy equivalence of inner cells is proposed, by which better results can be achieved with relatively smaller RVE. The validation of this method is justified by means of numerical examples of effective property predictions for materials with and without imperfections.
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