Mutual Sliding Motion of Wrapped Filaments for Biomedical and Engineering Applications

Abstract

Here we aim at understanding and modeling of macroscopic interactions and sliding motion of curved filaments during muscles’ isometric action in which tension is developed without overall contraction. A generic dynamic model of a curved elastic filament undergoing sliding, twisting, and unraveling around a cylindrical filament affected by the interfilament friction force is developed in full detail. In particular, the dynamic equations describing the general sliding motion of a curved filament wrapped around a cylindrical filament and pulled by a constant force applied to a free end are derived and solved numerically; the other end of the curved filament is considered to be fixed at the cylindrical one. The model predicts propagation of an elastic wave over the wrapped filament determined by the filament stiffness and the interfilament friction. The wrapped filament deformation and its ultimate arrest are predicted, and the final configurations of such filaments are revealed. Accordingly, the wrapped filament strain is predicted as a function of time for different values of the friction coefficient. The potential applications and possible biomechanical links of the proposed generic model are also discussed.