Beylergil, BertanUlus, HasanYildiz, Mehmet2026-01-242026-01-2420251229-91971875-0052https://doi.org/10.1007/s12221-025-01273-9https://hdl.handle.net/20.500.12868/5595In this study, we present a coupled, dimensional energy-balance model enhanced with machine-learning validation to predict residual-velocity curves and ballistic limits of fiber-reinforced composites. Projectile deceleration is described as a three-term balance involving strength-like, drag-like, and inertial effects, mapped to the nondimensional groups Pi(0), Pi(1), and Pi(2); closed-form and RK4 solutions yield residual velocity and regime boundaries (Pi(0) = Pi(1), Pi(1) = Pi(2)). Validation against six literature datasets (CFRP and aramid laminates; Vr-V0 curves) shows high accuracy: median R2 = 0.93-0.96 and typical RMSE = 10-30 ms(-)1, with best case R2 = 0.976 and RMSE = 6.99 ms(-)1 for thin CFRP. Ballistic-limit predictions accurately capture the nonlinear increase with thickness, with errors less than 1 ms(-)1 in brittle CFRP and up to 10 ms(-)1 in Kevlar laminates. A global master curve of wr = Vr/V0 versus parallel to Pi parallel to 2 collapses all data and shows a consistent trend. Energy-budget analysis quantifies the contributions of the three terms: the strength term Pi(0) dominates in about 90% of operational points, while drag-like effects are minimal and inertial effects only appear at thick or high-velocity limits; the dominance fractions and combined contributions support these shifts. The (V-0,h) regime map, derived by setting Pi(0) = Pi(1) and Pi(1) = Pi(2), separates design-relevant domains and aligns with observed transitions in Vr-V0 modes and slopes. An independent machine-learning check using Random Forests achieves R2 = 0.992, RMSE = 17.5 ms(-)1, and MAE = 12.4 ms(-)1 (fivefold cross-validation: R2 = 0.835 +/- 0.145), supporting the mechanistic hierarchy through feature importance. The integrated physics-based model and machine-learning analysis provide traceable parameters (alpha, beta, gamma), uncertainty bounds, and practical screening maps for composite and geometric options under high-velocity impact.eninfo:eu-repo/semantics/closedAccessComposite laminatesBallistic impactResidual-velocity predictionMechanistic modelingEnergy balance modelRandom Forest machine learningArticle10.1007/s12221-025-01273-92-s2.0-105023152167Q2WOS:001625277900001Q2