A hybrid electromechanical phase-field and deep learning framework for predicting fracture in dielectric nanocomposites

TL;DR

This work addresses the computational bottleneck of predicting crack evolution in electromechanically coupled dielectric nanocomposites by marrying a high-fidelity electromechanical phase-field fracture model with a CNN surrogate. It systematically compares learning crack paths from phase-field data versus electric potential fields using a ResNet‑U‑Net encoder–decoder, finding that electric potential distributions provide richer, smoother cues that yield higher segmentation accuracy and faster convergence. The study generates a large, physics-grounded dataset (10,000 FE simulations) from a fully coupled PF framework and trains CNNs to map geometry directly to crack paths, achieving near real-time predictions with IoU around 0.89–0.96 and F1 scores around 0.93–0.98 for potential data. The resulting 150× speed-up over high-fidelity simulations has clear implications for real-time SHM and design optimization in smart composites, and the authors outline futures paths including 3D extensions, PINNs, and multi‑modal sensing to further enhance robustness and applicability.

Abstract

The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an electromechanical phase-field fracture model with deep learning-based surrogate modeling to predict fracture evolution in dielectric nanocomposite plates. The underlying finite element simulations capture the coupling between mechanical deformation and electrical field perturbations caused by cracks, using a variational phase-field formulation. High-fidelity simulation outputs - namely, phase-field damage variables and electric potential fields -- are used to train convolutional neural networks (CNNs) with ResNet-U-Net architectures for pixel-wise segmentation of crack paths. The study systematically compares the performance of CNNs trained on phase-field versus electric potential data across multiple ResNet backbones. The results reveal that electric potential fields, although they encode damage indirectly, offer superior segmentation accuracy, faster convergence, and enhanced generalization, owing to their smoother gradient distribution and global spatial coverage. The proposed framework significantly reduces computational costs while preserving high accuracy, offers potential when appropriately adapted for sensor-based input data.

Figures (25)

• Figure 1: Schematic overview of the U-Net architecture employed for crack segmentation, adapted from Ref043.
• Figure 2: (Left) Model geometry and boundary conditions. (Right) finite element (FE) mesh.
• Figure 3: Representative simulations -- (Left) Reference/original configuration, (Middle) Phase-field crack path, and (Right) Electric potential crack path. Note: These plots are shown as standard false-color (RGB) contours for illustrative clarity; the actual data utilized for the deep learning framework are single-channel grayscale images derived from these distributions.
• Figure 4: Training and validation metrics for the ResNet34-based U-Net model on phase-field data -- (Left) Loss, (Middle) IoU, and (Right) F1-score.
• Figure 5: Training and validation metrics for the ResNet34-based U-Net model on electric potential data -- (Left) Loss, (Middle) IoU, and (Right) F1-score.