Modeling of discrete-continuous contact behaviors in multilevel helical structures

Abstract

Multiple contact problems within multilevel helical structures, characterized by both line (continuous) and point (discrete) contact states, have attracted significant attention. The local unique interplay of the multilevel helical structures arises from the periodic contact between entwined helices. The quantitative characterization of internal contact behavior has always been a challenging problem. Since the transposition contact characteristic is neglected, previous theoretical models are unable to directly solve local contact behaviors of multilevel helical structures. Herein, a theoretical model is developed to address discrete-continuous contact problems within multilevel helical structures under axial tension. This research primarily focuses on the explicit derivation of concise expressions for discrete and continuous contact forces. The theoretical model is established according to the general thin rod theory combining with the elastic Hertz contact formulation. The contact transmission formulation based on the action–reaction principle is introduced to capture the contact interplay between different structural levels. The normal contact stiffness (NCS) of multilevel helical structures is further calculated. Theoretical analysis and finite element (FE) simulations reveal that the transposition contact characteristic ensures that the discrete point contact force remains nearly constant along the axis of helical structures. This consistent point contact force enables the even distribution of external loads to each helix, thereby improving the load-bearing capacity. Further investigation highlights the critical role of a trade-off between dimensionless point contact force and NCS in determining the mechanical performance in multilevel helical structures. The effective prediction range of the present model covers geometric parameters of engineering sub-cables. The theoretical model effectively extends the classical Costello model to address complex contact problems within multilevel helical structures, providing valuable theoretical guidance for designing helical structures with superior normal contact stiffness and excellent load bearing capacity.