On the mechanics of biopolymer networks

In this thesis, we study the mechanical properties of biopolymer networks. We discuss which of these properties can be described by continuum approaches and which features, on the contrary, require consideration of the discrete nature or the topology of the network. For this purpose, we combine theoretical modeling with extensive numerical simulations. In Chapter 2, we study the elasticity of disordered networks of rigid filaments connected by flexible crosslinks that are modeled as wormlike chains. Under the assumption of affine deformations in the limit of infinite crosslink density, we show analytically that the nonlinear elastic regime in 1- and 2-dimensional networks is characterized by power-law scaling of the elastic modulus with the stress. In contrast, 3-dimensional networks show an exponential dependence of the modulus on stress. Independent of dimensionality, if the crosslink density is finite, we show that the only persistent scaling exponent is that of the single wormlike chain. Our theoretical considerations are accompanied by extensive quasistatic simulations of 3-dimensional networks, which are in agreement with the analytical theory, and show additional features like prestress and the formation of force chains. In Chapter 3, we study the distribution of forces in random spring networks on the unit circle by applying a combination of probabilistic theory and numerical computations. Using graph theory, we find that taking into account network topology is crucial to correctly capture force distributions in mechanical equilibrium. In particular, we show that application of a mean field approach results in significant deviations from the correct solution, especially for sparsely connected networks.