A Hybrid Physics-Informed Deep Learning Framework for Predictive Diagnostics of Concrete Fracture

This study presents a hybrid physics-informed deep learning framework for quantitative diagnostics of concrete cracks. Integrating finite element simulations with convolutional neural networks (CNNs), the model predicts key fracture mechanics parameters-Stress Intensity Factor ($K_I$) and Energy Release Rate (G-directly from stress-field images. Crucially, a custom loss function enforces the fundamental physical constraint $G=(\frac{K_I^2)}{E}$ during training, ensuring predictions are not only accurate but also physically consistent. Despite the constrained dataset ($n=50$), the model demonstrated stable convergence and successfully learned the underlying fracture patterns. Crucially, the enforced physical constraint $G=\frac{(K_I^2)}{E}$ proved highly effective as a powerful regularizer, which is evident in the controlled gap between the training and validation loss. The final test set evaluation yielded a Mean Absolute Error (MAE) of 3.7691. While this error is high due to data scarcity, the results successfully validate the framework's feasibility and physical fidelity, providing a trustworthy, first-principles-based tool for structural health monitoring beyond purely data-driven methods.