The feasible-fields method: A deep learning framework for progressive damage modelling of delamination under quasi-static loading

This paper presents the Feasible-Fields Method (FFM), a proof-of-concept of a hybrid machine learning (ML)-finite element (FE) framework for simulating delamination propagation in laminated polymer composites. The method investigates whether ML-predicted interface force fields can replace cohesive elements within an iterative FE procedure, while preserving comparable accuracy and improving robustness when larger load increments are used. Instead of employing cohesive elements, the FFM uses a physics-informed ML model to predict discrete force fields across the crack interface. These force fields are applied to the FE model, and the resulting deformation field is evaluated using a feasibility function based on crack tip separation and beam curvature. If the field is not feasible, the ML inputs are updated using gradient-based optimisation and a new force field prediction is generated. This process is repeated until a feasible deformation field is obtained. The framework is validated using moment-loaded double cantilever beam specimens. The results show that the FFM achieves high predictive accuracy, with mean absolute percentage errors below 1 % for both moment–rotation curves and crack tip propagation. The method reproduces cases representative of the training dataset, interpolates to unseen Young’s moduli, and adapts to tapered geometries not included during training. In addition, accurate responses are maintained with larger load increments, improving computational efficiency while avoiding the numerical oscillations and artificial stiffening observed in corresponding cohesive simulations. These results establish the Feasible-Fields Method as a viable proof of concept for embedding physics-informed ML predictions directly within an iterative FE framework for progressive delamination modelling.