Strength of filament bundles - The role of bundle structure stochasticity

Most biological fibrous materials are hierarchical, in the sense that fibers of finite length assemble in bundles, which then form networks with structural role. Examples include collagen, silk, fibrin and microtubules. Some artificial fiber-based materials share this characteristic, examples including carbon nanotube (CNT) yarns and unidirectional composites. Here we study bundles in which filaments do not break, while bundle rupture happens by the failure of inter-filament crosslinks, followed by pull-out. In all cases, the crosslinks are randomly distributed along interfaces. The strength of such bundles depends on material parameters of the filaments and crosslinks, such as their stiffness and strength, and on the cross-link density. We focus on the dependence of the bundle strength on two parameters: filament waviness and filament staggering. Bundles with regular staggering are stronger than those with stochastic staggering. We identify the optimal regular staggering that maximizes the strength. Filament waviness increases the strength of stochastically staggered bundles at constant crosslink density but decreases the strength of regularly staggered bundles. Results for bundles with permanent crosslinks, which never reform once they break, as well as transient crosslinks capable of reforming during deformation are presented, and it is shown that the general trends are independent of the nature of the crosslinks. The results are discussed in the context of collagen and carbon nanotube bundles.