This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples.

中文翻译：

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使用丰富的物理信息神经网络对二维有界异种材料进行界面裂纹分析

本研究探索了应用物理信息神经网络 (PINN) 来分析弹性双材料断裂力学背景下的界面裂纹问题。与均质材料中的裂纹相比，双材料界面裂纹表现出独特的行为，并且这种行为通常涉及振荡现象，这可能会给数值建模带来挑战。通过采用神经网络进行解逼近，PINN 是无网格的，并使用成批的配置点进行训练，这些配置点可以在计算域中随机或策略性地采样。为了有效捕获裂纹尖端区域的振荡奇异行为，本文引入了增强的 PINN 公式，该公式能够对界面裂纹进行建模，而无需在裂纹尖端附近进行任何细化。当前 PINN 的可训练参数在整个训练过程中动态优化，以满足底层微分方程和相关的初始/边界条件。目前 PINN 的显着优点之一是它使用富集函数来捕获裂纹区域周围的行为，从而在处理不规则或复杂的裂纹路径时具有更大的灵活性。该方法的准确性和稳定性经过多个基准示例的验证。