Flaw tolerant bulk and surface nanostructures of biological systems.

Abstract

Bone-like biological materials have achieved superior mechanical properties through hierarchical composite structures of mineral and protein. Gecko and many insects have evolved hierarchical surface structures to achieve extraordinary adhesion capabilities. We show that the nanometer scale plays a key role in allowing these biological systems to achieve their superior properties. We suggest that the principle of flaw tolerance may have had an overarching influence on the evolution of the bulk nanostructure of bone-like materials and the surface nanostructure of gecko-like animal species. We demonstrate that the nanoscale sizes allow the mineral nanoparticles in bone to achieve optimum fracture strength and the spatula nanoprotrusions in Gecko to achieve optimum adhesion strength. In both systems, strength optimization is achieved by restricting the characteristic dimension of the basic structure components to nanometer scale so that crack-like flaws do not propagate to break the desired structural link. Continuum modeling and atomistic simulations have been conducted to verify the concept of flaw tolerance at nanoscale. A simple tension-shear chain model has been developed to model the stiffness and fracture energy of biocomposites. It is found that, while the problem of low toughness of mineral crystals is alleviated by restricting the crystal size to nanoscale, the problem of low modulus of protein has been solved by adopting a large aspect ratio for the mineral platelets. The fracture energy of biocomposites is found to be proportional to the effective shear strain and the effective shear stress in protein along its path of deformation to fracture. The bioengineered mineral-protein composites are ideally suited for fracture energy dissipation as the winding paths of protein domain unfolding and slipping along protein-mineral interfaces lead to very large effective strain before fracture. The usual entropic elasticity of biopolymers may involve relatively small effective stress and may not be able to ensure simultaneous domain unfolding and interface slipping. Cross-linking mechanisms such as Ca++ induced sacrificial bonds in bone can increase the shear stress in protein and along the protein-mineral interface, effectively converting the behavior of entropic elasticity to one that resembles metal plasticity. The sacrificial bond mechanism not only builds up a large effective stress in protein but also allows protein deformation and interface slipping to occur simultaneously under similar stress levels, making it possible to engineer a very long range of deformation under significant stress in order to maximize energy absorption. Optimization of mineral platelets near theoretical strength is found to be crucial for allowing a large effective stress to be built up in protein via cross-linking mechanisms such as Ca++ induced sacrificial bonds. Similarly, for gecko adhesion, the strength optimization of individual spatulas is found to play a critical role in enhancing adhesion energy at the higher hierarchical level.