In this study, a novel approach that combines the principles of peridynamic
(PD) theory with PINN is presented to predict quasi-static damage and crack
propagation in brittle materials. To achieve high prediction accuracy and
convergence rate, the linearized PD governing equation is enforced in the
PINN's residual-based loss function. The proposed PD-INN is able to learn and
capture intricate displacement patterns associated with different geometrical
parameters, such as pre-crack position and length. Several enhancements like
cyclical annealing schedule and deformation gradient aware optimization
technique are proposed to ensure the model would not get stuck in its trivial
solution. The model's performance assessment is conducted by monitoring the
behavior of loss function throughout the training process. The PD-INN
predictions are also validated through several benchmark cases with the results
obtained from high-fidelity techniques such as PD direct numerical method and
Extended-Finite Element Method. Our results show the ability of the nonlocal
PD-INN to predict damage and crack propagation accurately and efficiently.

本研究提出了一种将弹性力学理论与 PINN 相结合的新方法，用于预测脆性材料中的准静态损伤和裂纹传播。通过将线性化的弹性力学方程强制加到 PINN 的基于残差的损失函数中，实现了高预测准确性和收敛速率。通过监测训练过程中损失函数的行为，对所提出的 PD-INN 模型的性能进行评估，并通过与 PD 直接数值方法和扩展有限元方法获得的结果进行验证。我们的结果表明，这种非局部 PDINN 能够准确高效地预测损伤和裂纹的传播。