The global mechanical response and local contact in multilevel helical structures under axial tension

Abstract

Multilevel helical structures are widely applied in engineering and biological areas with complicated local contact of interwire and global mechanical behaviors. Based on the thin rod theory, we propose a theoretical model which can simultaneously calculate the global mechanical properties and the local contact behaviors of the multilevel helical structure. By considering the contact deformation and the periodic kinematic parameters (the curvatures and twist) of the high order helix, the quasi-static solution of the multilevel helical structure is derived under axial tension, and two types of contact forces including line and point are analyzed. The multilevel contact transmission law is proposed to reveal the relationship between the contact forces with different types and levels, and the tendency of two contact forces with pitch can be obtained. Compared with the Costello model, the deviation of global mechanical responses and finite element (FE) simulations is reduced for the high-level helical structure. The local contact forces from FE simulations are in agreement with the predictions of the present model. The effect of the structural parameters on the global mechanical responses as well as the local contact forces are analyzed according to the present model. Finally, based on an engineering practical cable, the global mechanical responses and local contact behaviors of the simplified cable structure are predicted under axial tension. This study contributes to the understanding of the transmission mode and mechanism of contact forces in the multilevel helical structure.