The present work aims at the identification of the effective constitutive behavior of $$\Sigma 5$$ aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. The input for the ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations at the atomic scale for varying temperatures and loading conditions. The effective traction-separation relation is recorded during the MD simulations. The raw MD data then serves for the training of an artificial neural network (ANN) as a surrogate model of the constitutive behavior at the grain boundary. Despite the extremely fluctuating nature of the MD data and its inhomogeneous distribution in the traction-separation space, the ANN surrogate trained on the raw MD data shows a very good agreement in the average behavior without any data-smoothing or pre-processing. Further, it is shown that the trained traction-separation ANN captures important physical properties and is able to predict traction values for given separations not contained in the training data. For example, MD simulations show a transition in traction-separation behaviour from pure sliding mode under shear load to combined GB sliding and decohesion with intermediate hardening regime at mixed load directions. These changes in GB behaviour are fully captured in the ANN predictions. Furthermore, by construction, the ANN surrogate is differentiable for arbitrary separation and also temperature, such that a thermo-mechanical tangent stiffness operator can always be evaluated. The trained ANN can then serve for large-scale FE simulation as an alternative to direct MD-FE coupling which is often infeasible in practical applications.

中文翻译：

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人工神经网络在界面力学预测中的应用：晶界本构行为研究

本工作旨在通过使用机器学习（ML）技术，确定按比例加载的$$ \ Sigma 5 $$铝晶粒边界（GB）的有效本构行为。ML方法的输入是在变化的温度和负载条件下在原子尺度上具有挑战性的分子动力学（MD）模拟中收集的高精度数据。在MD模拟过程中记录有效的牵引分离关系。然后，原始的MD数据用于训练人工神经网络（ANN），作为晶粒边界本构行为的替代模型。尽管MD数据的波动性非常大，并且在牵引分离空间中分布不均匀，对原始MD数据进行训练的ANN代理在平均行为方面显示出非常好的一致性，而无需任何数据平滑或预处理。进一步地，示出了训练的牵引分离神经网络捕获重要的物理性质，并且能够针对训练数据中不包含的给定间隔预测牵引值。例如，MD仿真显示在剪切载荷作用下，牵引分离行为从纯滑动模式过渡到GB滑动和脱粘的组合，在混合载荷方向上具有中间硬化状态。GB行为的这些变化已在ANN预测中得到了充分体现。此外，通过构造，ANN替代物对于任意分离和温度而言都是可区分的，因此可以始终评估热机械切线刚度算子。