Discrete Modeling of the Mechanics of Entangled Materials

We employ a discrete computational model to study the entanglement transition of non-cross-linked semiflexible fibers during isostatic compressions. We determine, as a function of the fiber aspect ratio, packing densities and caging numbers, i.e., the density and number of contacts per fiber at the entanglement transition. The caging number is found to be 8 for short fibers and to drop down to 4 for longer fibers. Compressions beyond the entanglement transition allow us to determine, for these networks that deform primarily by bending, the scaling exponents of the pressure and of the bulk modulus (=3), as well as of the number of contacts per fiber (=1).