For multilayer structures in thin substrate systems, the interfacial failure is one of the most important reliability issues. The traction-separation relations (TSR) along fracture interface, which is often a complicated mixed-mode problem, is usually adopted as a representative of the adhesive interactions of a biomaterial system. However, the existing theoretical models lack complexity and are not able to fit with real-world TSRs obtained with end loaded split beam (ELS) experiments. The neural network fits well with the experimental data along the loading paths but fails to obey physical laws for area not covered by the training data sets, due to the lack of mechanics in pure neural network fitting with training data sets. In this paper, a thermodynamic consistent neural network (TCNN) is established to model the interface TSRs with sparse training data sets. Three thermodynamic consistent conditions are considered and implemented with neural network model. By treating these thermodynamic consistent conditions as constraints and implementing as loss function terms, the whole traction surface is constrained to provide reasonable results. The feasibility of this approach is approved by comparing the modeling results with different number of physical constraints. Moreover, the Bayesian optimization algorithm is adopted to optimize the weighting factors of the TCNN to overcome the convergence issue when multiple constraints are in present. The numerical implementation results demonstrated well behaved prediction of mixed-mode traction separation surfaces in terms of high agreement with experimental data and damage mechanics contained thermodynamic consistencies. The proposed approach opens doors to a new autonomous, point-to-point constitutive modeling concept for interface mechanics.

中文翻译：

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使用热力学一致神经网络 (TCNN) 对界面牵引分离关系进行数据驱动建模

对于薄基板系统中的多层结构，界面失效是最重要的可靠性问题之一。沿断裂界面的牵引分离关系（TSR）通常是一个复杂的混合模式问题，通常被用作生物材料系统粘附相互作用的代表。然而，现有的理论模型缺乏复杂性，无法与通过端载分束 (ELS) 实验获得的实际 TSR 相吻合。由于纯神经网络与训练数据集拟合缺乏力学，神经网络沿加载路径与实验数据拟合良好，但未能遵守训练数据集未覆盖区域的物理定律。在本文中，建立热力学一致神经网络 (TCNN) 以对具有稀疏训练数据集的接口 TSR 进行建模。考虑了三种热力学一致条件，并用神经网络模型实现。通过将这些热力学一致条件视为约束并作为损失函数项来实现，整个牵引表面被约束以提供合理的结果。通过比较不同数量物理约束的建模结果，验证了该方法的可行性。此外，采用贝叶斯优化算法优化TCNN的权重因子，克服存在多重约束时的收敛问题。数值实现结果表明，混合模式牵引分离面的预测与实验数据高度一致，损伤力学包含热力学一致性。所提出的方法为界面力学的新自主、点对点本构建模概念打开了大门。