Nanomechanics of biological systems - -what can we learn from nature about the principles of hierarchical materials?

Huajian Gao

Walter H. Annnenberg University Professor

Brown University

Abstract

The importance of mechanics and mechanical properties in biological functions has been widely recognized. The study on nanomechanics of biological systems is partly motivated by the observation that multi-level structural hierarchy is a rule of nature. Hierarchical structures/materials can be observed in all biosystems from chromosome, protein, cell, tissue, organism, to ecosystems. Mechanics of hierarchical materials inspired by nature may provide useful hints for materials engineering. Some questions of interest include: what are the roles and principles of structural hierarchy? what determines the size scales in a hierarchical material system? is it possible to design hierarchical materials with designated mechanical and other properties/behaviors? Specifically, natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures which seem to primarily serve their mechanical functions. The present talk will therefore be focused on the basic mechanics principles behind these hierarchical materials, including the principle of multiscale flaw insensibility. We perform detailed analyses on two idealized, self-similar models of hierarchical materials (“fractal bone” and “fractal gecko hair”), one mimicking the mineral-protein composite structure of bone and bon-like materials, and the other mimicking gecko’s attachment system, to demonstrate that structural hierarchy leads to simultaneous enhancement/optimization of multiple mechanical properties/functions such as stiffness, toughness, flaw tolerance and work of adhesion. In conventional homogeneous materials, the fracture energy is a material constant. In contrast, hierarchical materials do not have a unique fracture resistance, rather their fracture toughness depends on length scale: the bigger the scale, the larger the fracture resistance. This has been demonstrated by determining the traction-separation laws (cohesive laws) at different length scales in a hierarchical material.