Stochastic progressive damage modeling of composite laminates under fatigue loading

Fatigue-induced stiffness degradation in composite laminates is affected by nonlinear damage interactions and material variability. This paper presents a reduced-order uncertainty-propagation framework that couples Classical Laminate Theory, Continuum Damage Mechanics, tensile Hashin-type failure indices, an adaptive cycle-jump scheme, and Monte Carlo sampling. Separate longitudinal and transverse damage variables are evolved explicitly, while shear damage is linked consistently to these modes through D 6 = 1 − ( 1 − D 1 ) ( 1 − D 2 ) . The kinetic equations are integrated analytically over each cycle jump while the local stress state is held fixed, after which the laminate stiffness and ply stresses are recomputed. The scope of the present implementation is constant-amplitude tension–tension loading of symmetric and balanced laminates; it contains no endurance-limit threshold and its kinetic coefficients are specific to the adopted stress ratio and calibration benchmark. Five hundred simulations with fixed random seeds are used to propagate uncertainty in E 2 , Y T , and S L . The resulting bands are defined as pointwise central 95% percentile intervals, not confidence intervals or reliability bounds. A cross-ply case is presented as a calibration benchmark and an angle-ply [ ± 45 ] s case as a predictive numerical example. The results demonstrate the computational efficiency and mode sensitivity of the formulation while also identifying the experimental calibration and validation data required before reliability claims can be made.