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Abstract:
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.
