A numerical model for simulating mechanical behavior of flexible fibers

Abstract

A numerical method is developed for simulating the mechanical behavior of flexible fibers. A circular crossed fiber is represented by a number of cylindrical segments linked by spring dash-pot systems. Segments are lined up and bonded to each neighbor. Each bond can be stretched or compressed by changing the bond distance. Bending deflection and twist movement occur, respectively, in the bending and torsion planes. While the bending angle is determined by the positions of two neighboring bonds, a reference twist vector is introduced to record the torsion motion along the segment chain. Fluid drag forces are calculated based on the Stokes’ Law, where a free draining assumption is made. The motion of the fiber is determined by solving the translational and rotational equations of individual segments. Computer simulation has been conducted to verify the single fiber model with elastic theory and excellent agreements have been found between the simulation results and the theory in various situations such as beam deflection under static loads, vibrating cantilevers, and dynamics of helical shaped fibers. Examining orientations of rigid fibers in a viscous shear flow, simulation results suggest that the rotational time is sensitive to the fluid drag torque which is related to the shape of the segments. For highly flexible fibers, the effect of bending deformation on the period of rotation and the rotation orbits is also investigated. This numerical model for single flexible fibers linked by discrete segments provides a framework in the future studies on fibrous assemblies.