Multi-scale cohesive laws in hierarchical materials

Motivated by the observations that natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures, this paper aims to develop a better understanding of the effects of structural hierarchy on flaw insensibility of materials from the viewpoint of multi-scale cohesive laws. We consider two idealized, self-similar models of hierarchical materials, one mimicking gecko's attachment system and the other mimicking the mineral-protein composite structure of bone, to demonstrate that structural hierarchy leads to multi-scale cohesive laws which can be designed from bottom up to enable flaw tolerance from nanoscale to macroscopic length scales.