The Role of Friction in the Mechanics of Non-bonded Random Fiber Networks
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The Role of Friction in the Mechanics of Non-bonded Random Fiber Networks G. Subramanian1 and R. C. Picu1,2 1
Scientific Computation Research Center, Rensselaer Polytechnic Institute, 110 8th street, Troy, NY – 12180, U.S.A. 2 Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th street, Troy, NY – 12180, U.S.A. ABSTRACT The mechanics of systems of non-cross-linked fiber networks is studied in this work using a computational model inspired from the bead-spring models of polymeric melts. The fibers have random orientation and distribution in space, interact via stiff repulsive potentials and are characterized by their axial and bending stiffness. Fiber-fiber Coulombian friction is considered. The system is subjected to isostatic compression (strain control) and various statistical measures are evaluated. As the system is compacted, a critical density is reached at which stiffness develops. At this stage there is in average one fiber-fiber contact per fiber and the fiber free segment length has a uniform probability distribution function. Upon further compaction, the number of contacts per fiber increases and the segment length distribution becomes exponential. The respective cross-over densities depend on the fiber length and the friction coefficient. Significant hysteresis is observed upon loading-unloading in the total energy and the number of contacts per fiber. It is also observed that the distribution of contact energies in the range of densities where the system forms a topological network is a power law. INTRODUCTION The mechanics of an entangled assembly of randomly oriented fiber-networks is of relevance to many sub-fields of materials science, such as paper, fabrics, and battery substrates. Scaffolds and crosslinked protein filaments have received a great deal of attention [1]. The eukaryotic cellular cytoskeleton is now increasingly understood as a complex dynamic structure whose functioning involves mechanics. Random fiber networks may be cross-linked or just entangled. Intermediate configurations in which the network is primarily entangled, but a small density of cross-links exists are also of physical relevance. Rubber and various gels are molecular networks and varying the density of cross-links controls the stiffness and internal dissipation of the material. While there is a substantial body of literature devoted to randomly bonded (cross-linked) fiber networks [2], the (non-molecular) entangled networks are much less studied. Even less understood is the mechanics of a fiber network in presence of inter-fiber friction. The deformation of clumps of fibers, wool and metallic filaments has been studied experimentally [34]. Modeling work has been primarily focused on how the system responds to compaction: the evolution of the number of contacts per fiber and the effective stiffness of the clump as the system is being compressed hydrostatically (density increases) has been modeled [5-6]. Nevertheless, the dynamics associated with entangled fib
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