Nonaffine Behavior of Three-dimensional Semiflexible Polymer Networks

Three-dimensional semiflexible polymer networks are the structural building blocks of various biological and structural materials. Previous studies have primarily used two-dimensional models for understanding the behavior of these networks. In this paper, we develop a three-dimensional nonaffinity measure capable of providing direct comparison with continuum level homogenized quantities, i.e., strain field. The proposed nonaffinity measure is capable of capturing possible anisotropic microstructures of the filamentous networks. This strain-based nonaffinity measure is used to probe the mechanical behavior at different length scales and investigate the effects of network mechanical and microstructural properties. Specifically, it is found that although all nonaffinity measure components have a power-law variation with the probing length scale, the degree of nonaffinity decreases with increasing the length scale of observation. Furthermore, the amount of nonaffinity is a function of network fiber density, bending stiffness of the constituent filaments, and the network architecture. Finally, it is found that the two power-law scaling regimes previously reported for two-dimensional systems do not appear in three-dimensional networks. Also, unlike two-dimensional models, the exponent of the power-law relation depends weakly on the density of the three-dimensional networks.