Hierarchical fiber bundle model to investigate the complex architectures of biological materials

The mechanics of fiber bundles has been widely studied in the literature, and fiber bundle models in particular have provided a wealth of useful analytical and numerical results for modeling ordinary materials. These models, however, are inadequate to treat bioinspired nanostructured materials, where hierarchy, multiscale, and complex properties play a decisive role in determining the overall mechanical characteristics. Here, we develop an ad hoc hierarchical theory designed to tackle these complex architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The roles of finite size, twisting angle, and friction are also included. Size effects on the statistical distribution of fiber strengths naturally emerge without invoking best-fit or unknown parameters. A comparison between the developed theory and various experimental results on synthetic and natural materials yields considerable agreement.