Models for stiffening in cross-linked biopolymer networks: A comparative study

In a recent publication, we studied the mechanical stiffening behavior in two-dimensional (2D) cross-linked networks of semiflexible biopolymer filaments under simple shear. These simulations make use of a geometrically nonlinear finite-element technique, taking into account the discreteness of the biopolymer network. As an alternative to the prevalent view, these computations relate the stiffening to nonaffine network reorientations. However, this discrete-network model neglects any interaction of the filaments with the surrounding fluid, which is the origin of entropic stiffening in single filaments and in biopolymer networks. For this reason, this article is devoted to a thorough study of the difference between both approaches on the 2D single-filament level. In addition, we investigate the deviation from affine deformation behavior, by comparing the discrete calculations with an affine-network model.