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 引用本文: 白晓伟, 赵鲁阳, 李亮, 罗利龙, 阳杰, 胡衡. 两类数据驱动计算均匀化方法对比研究. 力学学报, 2024, 56(7): 1931-1942.
Bai Xiaowei, Zhao Luyang, Li Liang, Luo Lilong, Yang Jie, Hu Heng. Comparative study on two types of data-driven computational homogenization methods. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 1931-1942.
 Citation: Bai Xiaowei, Zhao Luyang, Li Liang, Luo Lilong, Yang Jie, Hu Heng. Comparative study on two types of data-driven computational homogenization methods. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 1931-1942.

## COMPARATIVE STUDY ON TWO TYPES OF DATA-DRIVEN COMPUTATIONAL HOMOGENIZATION METHODS

• 摘要: 目前针对非均质材料与结构的多尺度仿真尚面临本构建模复杂和多尺度计算成本高的难题. 数据驱动计算均匀化方法一方面通过数据科学的手段降低与本构模型相关的人力和时间成本, 另一方面将耗时的细观问题计算移至线下进行, 从而显著提升非均质材料与结构的在线计算效率. 该方法按控制方程的来源可大致分为两类: 第一类是基于能量泛函的数据驱动算法, 旨在通过人工智能手段高效地获取材料本构关系, 继而在经典计算力学框架下通过能量极值求解问题; 第二类是基于距离泛函的数据驱动算法, 其绕开材料本构建模过程, 直接利用本构数据中的点与满足守恒方程的点的距离极值寻求问题的解. 文章简要回顾两类数据驱动计算均匀化方法的求解思路, 以纤维增强复合材料结构为例, 分别从定性和定量的角度分析样本数据量对两类算法计算效率和精度的影响, 继而从算法实现、计算精度、计算效率和后处理等方面进行对比分析, 探讨两者在求解多尺度问题时的优势与不足, 以期为发展高效的非均质材料结构分析技术提供参考.

Abstract: Nowadays the simulation methods for heterogeneous materials and structures are still faced with challenges of complex constitutive modeling and costly multiscale computation, which are expected to be overcome by the emerging data-driven computational homogenization methods. Data-driven computational homogenization method aims to save the labor and time costs for constitutive modeling by means of data science. In the meanwhile, it is able to considerably enhance the online computational efficiency for simulating heterogeneous materials and structures by shifting numerous mesoscopic calculations to the offline stage. Data-driven computational homogenization methods can be roughly summarized into two categories according to the functionals to be solved. The first one is based on energy functional, whose key point is to efficiently capture constitutive relation using artificial intelligence and then obtain the solution in the framework of classical computational mechanics. The other one is based on distance functional, whose specificity lies in directly embedding the material data into mechanical simulations. The extremum of distance functional is used to find the state from the constitutive data set that is closest to satisfying the conservation laws, thus bypassing the step of empirical material modeling. The outline of this paper is organized as follows. At first, the basic procedures for conducting multiscale simulations through above two data-driven computational homogenization methods are briefly recalled. Next, numerical simulations concerning the fiber-reinforced composite structure are conducted by adopting both methods. Based on the obtained results, the influence of the number of data points on the computational efficiency and accuracy is evaluated from both qualitative and quantitative perspectives. Finally, the superiorities and weaknesses of both algorithms for conducting multiscale simulations are discussed in terms of different aspects, such as the algorithm implementation, computational accuracy, computational efficiency and post-processing. The outcomes of this paper are expected to offer theoretical basis for developing techniques to efficiently simulate heterogeneous materials and structures.

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