Atomistic and Continuum Studies of Flaw Tolerant Nanostructures in Biological Systems
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ATOMISTIC AND CONTINUUM STUDIES OF FLAW TOLERANT NANOSTRUCTURES IN BIOLOGICAL SYSTEMS Markus J. Buehler1*, Haimin Yao2, Baohua Ji3, Huajian Gao2, 1 California Institute of Technology, Pasadena, 91125, CA, USA 2 Max Planck Institute for Metals Research, D-70569 Stuttgart, Germany 3 Tsinghua University, Beijing, China. ABSTRACT 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 atomisticcontinuum 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. INTRODUCTION In this article, we focus on fundamental design concepts of structural links in biological bulk and surface materials and verification using multi-million atomistic simulations. Once characteristic materials length scales are reduced to nanoscale, mechanical properties often change dramatically. Nature is the unrivaled master in building and using nanodevices to perform different tasks ranging from energy transport, to assembling machines, or to complex control systems far beyond what human beings have ever been able to create. In this paper, we
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Corresponding author, E-Mail: [email protected]
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Figure 1: Left: Microstructure of bone-like biological materials. Such materials typically consist of
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