Modeling the mechanics and failure of discrete viscoelastic fiber networks

Abstract

Network problems arise in all aspects of bioengineering, including biomechanics. For decades, the mechanical importance of highly interconnected networks of macromolecular fibers, especially collagen fibers, has been recognized, but models at any scale that explicitly incorporate fiber-fiber interactions into a mechanical description of the tissue have only started to emerge more recently. The mechanical response of networks shows an inherent non-linearity arising from the network architecture, and the non-affine deformations occurring within it. Thus, the overarching goal of this dissertation was to model the steady-state and time-dependent behaviors of discrete fiber networks to understand better how the behavior of an individual fiber differs from that of a network, and to study the effect of a network’s structure on its mechanics. First, viscoelastic relaxation of networks composed of linear viscoelastic fibers was analyzed, throwing light on two different contributions to the network re- laxation process: a material contribution due to the intrinsic viscoelasticity of the fibers, and a kinematic contribution due to the structure of the network. The effect of network composition on its relaxation spectrum was also analyzed revealing a constant evolution of structure-dependent characteristic relaxation times with changing composition. Next, network fatigue behavior was modeled using a fiber-based cumulative damage model to obtain stress-life (SN) curves for the network, and to compare fatigue behaviors of different network structures. Finally, the network model was used in a multiscale finite element approach to model actin-myosin motor-driven cell cytoskeletal contraction. The multiscale model was also used to highlight the importance of the choice of microstructure in predicting tissue pre-failure and failure behaviors.