Analysis of microstructure uncertainty propagation in fibrous composites Empowered by Physics-Informed, semi-supervised machine learning

The advancements in multi-scale computational analysis of fiber reinforced composites have led to the possibility of predicting important material properties based on their microstructure characteristics. Nevertheless, major challenges remain. The fiber distributions feature inherent randomness, which naturally leads to variations in properties such as transverse strength. This in turn undermines the significance of deterministic analysis to guide manufacturing optimization. Direct Monte Carlo simulation for uncertainty analysis is computationally insurmountable, as a single run of finite element simulation is already costly. While several surrogate modeling techniques leveraging supervised learning have been explored, it is commonly recognized that the efficacy of these surrogate models hinges upon the size of training dataset. In this research we establish a semi-supervised learning framework that can produce highly accurate emulation results with much reduced size of labeled training dataset. A random fiber packing algorithm is employed to sample the representative volume element (RVE) images that are subsequently fed to the finite element analysis to generate the ground-truth labeled data used in the training of neural network. To reduce the ground-truth labeling cost while maintaining the deep learning capacity. we employ the pseudo labeling technique where the base model is initially trained on a small set of ground truth labeled data and then used to generate credible pseudo-labels for a larger pool of unlabeled data. The model is subsequently retrained on this augmented dataset with adjusted weights and biases to reflect the varying confidence in the label sources. This framework is successfully employed in the analysis of microstructure uncertainty propagation in fibrous composites. The proposed approach efficiently leverages patterns from both unlabeled and limited labeled samples to predict transverse strength for varied RVE samples, matching the efficacy of a fully supervised model trained with 1,000 ground truth labels while simultaneously slashing labeling efforts by 72%. This framework can be extended to uncertainty propagation analysis using microstructure characteristics of other materials.