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Modeling Flexible Fiber-Motion and Orientation: Comparison Between Classical Rigid Fiber Models and the Rod-Chain Model
Objective and Background
Long fiber reinforced composites play a significant role in various industrial applications. Understanding hoMotion of a single flexible fiber.w fiber configuration changing in the polymer matrix during processing influences the properties of the final composites is critical for material design as well as material property control. By using modeling and numerical methods to simulate the material manufacturing process, material properties can be predicted in a way of much lower cost and higher efficiency compared to experimental methods. There have been several models proposed trying to acquire the evolution of long fiber motion and orientation in polymer flow during processing, among which rod chain model by representing a single long fiber as a series of perfectly rigid rods, each of which made of a certain number of beads, was verified to be of reasonable efficiency and simple construction based on fluid  dynamics. The objective of this research is to develop a mathematical model to simulate the motion of a large number of long flexible fibers in various flow conditions, based on which various bulk material properties at any time of processing are predicted by the properties of component materials and initialconditions of processing.
Developed Results
Flexible fiber model employed in the present study (shown in the figure below) is that of Wang et al. (European Journal of Mechanics B/Fluids 25 (2006) 337–347), where the flexible fiber is composed of a series of rigid beads forming individual rods and the rods are connected by torque and force joints (hinges).
Flexible fiber model schematic.
Rod chain model yields the same results as that obtained from Jeffery’s equation with respect to fiber motion period and orbits when fiber is perfectly rigid.  This is demonstrated in the figure below where the motion is compared for a flexible and a rigid fiber (a) N = 1, Nr = 10, ar = 10, E⁄(ηγ̇)=2105, rc = 21.13, initial unit direction vector p = [1 0 0]T, (b) N = 1, Nr = 30, ar = 30, E⁄(ηγ̇)=2103, rc = 4.75, initial unit direction vector p = [1 0 0]T.
Comparison between flexible fiber model and Jeffery motion

Publications From This Work
  • Flexible Fiber Waviness as a Role in Fiber Motion Simulation and Material Property Prediction. C. Zhang* and D.A. Jack. Early Career Technical Conference, Fayetteville, Arkansas, March 2011.
  • Fiber Orientation for Suspensions of Long Fibers: Comparison of Rigid and Flexible Models. C. Zhang* and D.A. Jack. Proceedings of the Society of Rheology's 82nd Annual Meeting, Santa Fe, New Mexico, October, 2010.
  • Modeling of Flexible Fiber Motion and Orientation in Simple Shear Flow: A Comparison between Rod-Chain Model and Jeffery's Equation. C. Zhang* and D.A. Jack. Proceedings of ASME IMECE'10, Vancouver, British Columbia, Canada, November, 2010.
  • Flexible Fiber Suspension Orientation Model Predictions: Comparison Between Rod-Chain Model and Classical Jeffery's Rigid Ellipsoid Model. C. Zhang* and D.A. Jack. Early Career Technical Conference, Tulsa, Oklahoma, March 2010.
Baylor University School of Engineering and Computer Science Department of Mechanical Engineering Sic'Em - Scientific Innovations in Composites and Engineering Materials