An efficient semi-analytical method for modeling contacts in multilayer helical strand cables under microslip conditions

Abstract Multilayer cables are extensively used owing to their high strength, flexibility, and durability. Under external forces, cyclic loadings induce slip and microslip at strand contact points, leading to fretting, fatigue, wear, and ultimately strand failure. Accurate identification of regions prone to these phenomena requires the determination of normal and tangential traction distributions, stick–slip–microslip zones, local sliding distances, and subsurface stress fields. However, the large number of simultaneous contact points in multilayer cables makes numerical modeling computationally expensive. This study presents a semi-analytical approach for efficiently determining the normal and tangential traction distributions at strand contact interfaces, as well as the corresponding stick and microslip zones associated with fretting. The model is based on the half-space Boussinesq force–displacement relationships for normal and tangential point loads and achieves high accuracy with significantly reduced computation times. Comparisons with experimental data and finite element method simulations demonstrates that the proposed model accurately predicts traction distributions and internal stresses while reducing computation time by a factor exceeding 375. The approach effectively captures non-Hertzian contact behavior under combined normal and tangential loading, enabling large-scale analysis of multiple contact points in multilayered cables. Furthermore, the model supports rapid wear simulations and integrates the Smith–Watson–Topper criterion for fatigue evaluation. Validation against experimental observations confirms its robustness, general applicability, and high computational efficiency for both new and worn strands.