Interface crack analysis in 2D bounded dissimilar materials using an enriched physics-informed neural networks

Abstract

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.