Bone-like biological materials have achieved superior mechanical properties through hierarchical composite structures of mineral and protein. Geckos and many insects have evolved hierarchical surface structures to achieve superior adhesion capabilities. What is the underlying principle of achieving superior mechanical properties of materials? Using joint atomistic-continuum modeling, we show that the nanometer scale plays a key role in allowing these biological systems to achieve such properties, and suggest that the principle of flaw tolerance and design for robustness 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 illustrate that if the characteristic dimension of materials is below a critical length scale on the order of several nanometers, Griffith theory of fracture no longer holds. An important consequence of this finding is that materials with such nano-substructures become flaw-tolerant, as the stress concentration at crack tips disappears and failure always occurs at the theoretical strength of materials, regardless of defects. The atomistic simulations complement continuum analysis and reveal a smooth transition between Griffith modes of failure via crack propagation to uniform bond rupture at theoretical strength below a nanometer critical length. This modeling resolves a long-standing paradox of fracture theories, and these results have important consequences for understanding failure of small-scale materials. Additional investigations focus on shape optimization of adhesion systems. We illustrate that optimal adhesion can be achieved when the surface of contact elements assumes an optimal shape. The results suggest that optimal adhesion can be achieved either by length scale reduction, or by optimization of the contact shape. Whereas change in shape does not lead to robustness, reducing the dimension results in robust adhesion devices.
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