FE${}^\ extbf{ANN}$ $-$ 一种基于物理约束神经网络与自动化数据挖掘的高效数据驱动多尺度方法
FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
AI总结：
提出FE${}^\ ext{ANN}$框架，结合物理约束神经网络与自主数据挖掘，实现高效多尺度模拟，减少微观模拟次数，适用于各向异性非线性超弹性材料。
摘要：
本文提出了一种新的数据驱动多尺度框架，称为FE${}^\ ext{ANN}$，其基于两个关键支柱：使用物理约束人工神经网络（ANNs）作为宏观代理模型，以及自主数据挖掘过程。该方法能够高效模拟具有复杂微观结构且在宏观尺度上表现出各向异性和非线性行为的材料。目前，我们仅考虑有限应变超弹性问题。通过使用一组特定于问题的不变量作为ANN的输入，并以Helmholtz自由能密度作为输出，若干物理原理（如客观性、材料对称性、角动量平衡兼容性和热力学一致性）得以先验满足。训练基于ANN的代理模型所需的数据（即宏观变形和相应应力）通过代表性体积单元（RVEs）的计算均匀化收集。该方法的核心理特征是，在整体循环中完全自主地挖掘所需数据集。在循环的每次迭代中，通过从宏观有限元（FE）模拟中收集宏观变形状态，并随后根据所考虑材料的各向异性类别进行排序来生成新数据。最后，所有未知变形均在RVE模拟中规定，以获得相应应力，从而扩展数据集。因此，所提出的框架能够将耗时的微观尺度模拟次数减少到最低。该方法示例性地应用于几个描述性示例，其中考虑了具有高度非线性Ogden型行为的纤维增强复合材料。
英文摘要：
Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e.g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i.e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element (FE) simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
