Micromechanical simulations of biopolymer networks with finite elements

The mechanics of biological tissue is largely determined by the mechanics of biopolymer networks such as the extracellular matrix on cellular scale or the cytoskeleton on subcellular scale. Micromechanical simulations of biopolymer networks have thus attracted increasing interest in the last years. Here we introduce a simulation framework for biopolymer networks based on a finite element model of the filaments with a backward Euler time integration scheme. This approach surpasses previously published ones, especially those based on bead-spring models, by its sound theoretical foundation, a great flexibility, and at the same time an efficiency gain of approximately two orders of magnitude. Thereby it allows for addressing problems no previous numerical method could deal with, e.g., the micromechanical analysis of the viscoelastic moduli of crosslinked biopolymer networks in the low frequency regime or the analysis of the thermal equilibrium phases of such networks. By means of several examples it is discussed how this capacity can be exploited in multiscale simulations of biological tissue on cellular and subcellular scale.