A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses, strains, strain rates, failure stress, material degradation, and anisotropy which has not been used before. DDFEM is implemented in the context of linear elements of a nonlinear elastic solid. The presented framework can be used for variety of applications by directly using experimental data. This has been demonstrated by using the DDFEM framework to predict deformation, degradation and failure in diverse applications including nanomaterials and biomaterials for the first time. DDFEM capability of predicting unknown and unstructured dataset has also been shown by using Delaunay triangulation strategy for scattered data having no structure or order. The framework is able to capture the strain rate dependent deformation, material anisotropy, material degradation, and failure which has not been presented in the past. The predicted results show a very good agreement between data set taken from literature and DDFEM predictions without requiring to formulate complex constitutive models and avoiding tedious material parameter identification.

中文翻译：

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数据驱动的有限元方法：理论与应用

在这项工作中提出了一种数据驱动的有限元方法 (DDFEM)，它考虑了两个以上的材料状态变量。DDFEM 框架受 (1,2) 启发，可以解释多个状态变量，即。应力、应变、应变率、失效应力、材料退化和以前没有使用过的各向异性。DDFEM 是在非线性弹性实体的线性单元的上下文中实现的。通过直接使用实验数据，所提出的框架可用于各种应用。这已经通过使用 DDFEM 框架首次预测包括纳米材料和生物材料在内的各种应用中的变形、降解和失效而得到证明。通过对没有结构或顺序的分散数据使用 Delaunay 三角剖分策略，还显示了 DDFEM 预测未知和非结构化数据集的能力。该框架能够捕捉到应变率相关的变形、材料各向异性、材料退化和失效，这在过去没有出现过。预测结果表明，从文献中获取的数据集与 DDFEM 预测之间具有非常好的一致性，无需制定复杂的本构模型并避免繁琐的材料参数识别。