Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 99536

99536 - Mechanisms of Force Transmission in Fiber Networks 

Fiber networks are the primary structural components of many biological materials as well as several synthetic materials including nonwovens, hydrogels and paper. Fiber networks, particularly those with fibers soft in bending, exhibit global nonlinearities such as stiffening due to extension, and softening due to compression. Some of the local mechanisms leading to these global behaviors are well studied; for example, it is known that fibers align with the direction of applied tension during strain stiffening and buckle during compression softening.  Interestingly, networks stiffen along directions different from the fiber alignment as well, but the underlying local deformation mechanisms have been studied primarily from a qualitative perspective and, hence, are not yet clear.  The incomplete understanding of the key mechanisms connecting the local microstructural evolution to the global mechanical behavior makes the prediction of the global mechanics qualitative rather than precise. To fill in this gap, we studied how axial forces are transmitted inside the fiber network. At the level of the fibers, force transmission occurs along paths called force chains, which originate from the load source and continuously evolve during the course of deformation. We developed methods to quantify the force chains, enabling us to examine their contributions to strain-stiffening. We performed numerical simulations on two-dimensional networks of random and aligned fibers, modeling the fibers using three-node beam elements in finite element software. Uniaxial extension was applied in combination with shearing to quantify the small-strain modulus and the critical strain for strain-stiffening. To identify the force chains, we set a threshold for axial force in the fibers and identified all chains of connected fibers for which the axial force was larger than the threshold. To quantify the force chains, we computed the total length of all force chains. We studied the evolution of force chains by taking the derivative of the total length of force chains with respect to the applied nominal strain. Results showed that the total lengths of force chains were strongly correlated with the small-strain modulus of the fiber network and that the highest rate of evolution of force chains coincided with the global critical strain for strain-stiffening of the fiber network. Therefore, force chains are important factors in connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network. Finally, we verified some of the simulation results by performing mechanical tests on a 3D-printed fiber network matching one used in the simulations.

Presenting Author: Mainak Sarkar University of Wisconsin-Madison

Presenting Author Biography: Mainak Sarkar is a third-year PhD student in Engineering Mechanics at UW-Madison working with Professor Jacob Notbohm on mechanics of fibrous materials. He has done Bachelor in Civil Engineering from Jadavpur University, India and Master's in Structural Engineering from Indian Institute of Science, Bangalore, India.

Authors:

Mainak Sarkar University of Wisconsin-Madison
Jacob Notbohm University of Wisconsin-Madison