Bio-inspired mechanics of bone-like hierarchical materials

Abstract

Nanotechnology promises to enable mankind to design materials hierarchically via a bottom-up approach, i.e. by tailor-designing materials from atomic scale and up. However, currently we barely have any theoretical basis on how to design a hierarchical material to achieve a particular set of macroscopic properties. To demonstrate the potential of bottomup design, we consider a model material with self-similar hierarchical structures mimicking the elementary structure of bone. The resulting "fractal bone" exhibits a similar structure at each hierarchical level consisting of staggered hard plates aligned in a soft matrix. Simple analytical models are adopted to evaluate the stiffnesses, strengths and fracture energies of all hierarchical levels. The hierarchical structural sizes are determined based on the principle of flaw tolerance. It is shown that the bottom-up designed fractal bone can tolerate crack-like flaws from nanoscale all the way to macroscopic scales without size limit. © 2007 Springer.