Random-walk-based stochastic modeling of three-dimensional fiber systems

For the simulation of fiber systems, there exist several stochastic models: systems of straight nonoverlapping fibers, systems of overlapping bending fibers, or fiber systems created by sedimentation. However, there is a lack of models providing dense, nonoverlapping fiber systems with a given random orientation distribution and a controllable level of bending. We introduce a new stochastic model in this paper that generalizes the force-biased packing approach to fibers represented as chains of balls. The starting configuration is modeled using random walks, where two parameters in the multivariate von Mises-Fisher orientation distribution control the bending. The points of the random walk are associated with a radius and the current orientation. The resulting chains of balls are interpreted as fibers. The final fiber configuration is obtained as an equilibrium between repulsion forces avoiding crossing fibers and recover forces ensuring the fiber structure. This approach provides high volume fractions up to 72.0075%.