A hybrid offline-online model order reduction approach for damage propagation problems

Accurately modelling damage propagation in composites with 3D explicit finite element methods requires high-dimensional models, making simulations computationally prohibitive. Conventional reduced-order models (ROMs) trained offline are ineffective for fracture problems, since stress redistribution and crack growth cannot be anticipated a priori. In this work, a hybrid offline–online ROM that couples elastic-only offline training with adaptive online enrichment of the reduced basis during damage evolution is introduced. Proper Orthogonal Decomposition (POD) is combined with Energy-Conserving Mesh Sampling and Weighting (ECSW) and Gappy data reconstruction to achieve efficient time integration with 3D solid and cohesive elements. Unlike existing domain decomposition approaches, the proposed framework does not require prior knowledge of crack paths and can refine the basis anywhere in the domain as damage develops. The method is demonstrated on open-hole tensile tests at two distinct length scales, capturing delamination, fibre failure and failure stress with good accuracy when compared to full-order simulations and experiments. Improved computational savings are achieved, with efficiency gains increasing with model size. These results establish the hybrid ROM as a scalable and general approach for modelling distributed, path-dependent fracture in composite materials.