Staggered prediction machine learning models for crack propagation forecasting in particle-reinforced composites

Numerical simulation of fracture in particle-reinforced composites is computationally intensive, whereas machine learning frameworks offer a pathway for rapid prediction of crack propagation and field variable monitoring. To achieve physically motivated predictions, this work establishes two physics-inspired deep learning frameworks drawing architectural inspiration from the staggered solution scheme in the finite element method. Unlike purely data-driven approaches, the proposed models integrate the tensile energy density as the driving force alongside Mises stress and the phase field. Two staggered prediction models are investigated: a series forecasting model and a physics-enhanced multi-channel-input model. By iteratively updating stress equilibrium, energy superposition and damage evolution, these models capture the path-dependency of fracture. Comparative results demonstrate that while both models achieve high accuracy, the multi-channel-input model, which synergizes the driving force with stress distribution and crack morphology, exhibits superior training efficiency and generalization. It effectively captures the bi-directional feedback between driving force and damage topology, enabling accurate forecasting of complex crack paths and interface debonding in heterogeneous composites.