Homogenization analysis is widely used to derive effective macroscopic properties of composite materials instead of experimental characterization. However, this approach is computationally demanding. To address this challenge, we aim to (i) derive a reduced basis homogenization method (RBHM) to vector-valued partial differential equations (PDEs), addressing a gap in predicting homogenized elastic properties of unidirectional composites; (ii) develop an offline–online strategy to evaluate reduced basis (RB) corrector gradients; (iii) validate the homogenized material properties obtained by the RBHM with experimental data, unlike previous works that relied solely on numerical comparisons; and (iv) apply the RBHM to two rectangular and one hexagonal unit cell configurations, representing the unidirectional composites. We demonstrate the utility of the proposed RBHM through parametric studies that explore the variation of the homogenized thermal and elastic properties with respect to the thermal conductivity and elastic properties of matrix and fiber materials. In conclusion, the reduced basis method (RBM) combined with the homogenization method (HM) are efficient compared to the corresponding finite element method (FEM) while generating minimal errors.

中文翻译：

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减少周期性复合材料的热性能和弹性性能的基均匀化


均质分析被广泛用于推导复合材料的有效宏观特性，而不是实验表征。但是，这种方法对计算要求很高。为了应对这一挑战，我们的目标是 （i） 推导出一种简化的基均质化方法 （RBHM） 到向量值偏微分方程 （PDE），解决了预测单向复合材料均质弹性特性的差距;（ii） 开发离线-在线策略来评估降低基数 （RB） 校正子梯度;（iii） 用实验数据验证 RBHM 获得的均质材料特性，这与以前仅依赖于数值比较的工作不同;（iv） 将 RBHM 应用于两个矩形和一个六边形晶胞配置，代表单向复合材料。我们通过参数研究证明了所提出的 RBHM 的实用性，这些研究探索了均匀热和弹性特性相对于基体和纤维材料的热导率和弹性特性的变化。总之，与相应的有限元法 （FEM） 相比，简化基法 （RBM） 与均质法 （HM） 相结合是有效的，同时产生的误差最小。