Cracking composite design: Trace-driven scaling for cluster-based universal design

Traditional composite design requires bespoke material characterization and layup optimization for every new fiber–matrix system, creating significant delays and costs. We introduce a physics-based, trace-scaling framework that collapses hundreds of fiber–matrix–volume-fraction combinations into mechanically equivalent π -clusters, each defined by three non-dimensional stiffness ratios. By invoking Buckingham’s π -theorem, we show that materials with the same π -values share nearly identical normalized stiffness matrices, so their absolute stiffness scales only with the trace of the matrix. This finding overturns the notion of a “universal master-ply”, demonstrating instead that each π -cluster demands its own master-ply. A comprehensive sensitivity study, using Frobenius, eigenvalue, and spectral norms, reveals that G 12 / E 1 dominates the variability in mechanical response. We validate our method on 1 014 fiber–matrix–volume-fraction systems, applying K-means clustering in π -space to identify three robust clusters. Within each cluster, a single master-ply, defined as the centroid of the cluster, predicts the buckling loads of all cluster’s members with the error < 3 % , while the cross-cluster transfer incurs a much higher error. By restricting design to π -clusters, universal scaling laws emerge naturally, slashing optimization effort and enabling rapid, generalizable layup design for UD, woven, and hybrid composites alike. Finally, our approach recasts material selection and layup optimization into a unified, physics-grounded framework. • Dimensionless clustering of composites : Hundreds of fiber–matrix–volume fraction combinations collapse into three equivalent π -clusters, simplifying composite design. • Cluster-based master plies : A centroid-optimized layup accurately predicts buckling within each cluster (¡3% error). • Exclusive design domains : Cross-cluster transfers lead to > 15% deviation, confirming cluster-specific applicability. • Reduced design complexity : The framework enables scalable, data-driven composite optimization across material families.