Mechanics of Nanoscale and Hierarchical Structures of Biological Materials: Flaw Tolerant Strategies in Nature
Professor Huajian Gao, who had served as a director at the Max Planck Institute for Metals Research during the last 5 years and is now moving to the Division of Engineering of Brown University, has been working with collaborators on mechanics of bottom-up designed nanocale and hierarchical structures of biological materials such as bone and gecko . This research has revealed several key mechanics concepts and principles that underline a wide variety of biological systems. The following is a report of his research on bio-inspired flaw tolerant strength theory.
On the hierarchical biomechanics of bone, Gao has aimed to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. Gao has posed the following questions of interest to mechanics: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material (protein)? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material (mineral)? (4) The strength question: how does nature balance the widely different strengths of protein and mineral ? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures?
What is the role of structural hierarchy? Anyone who is interested in these questions can read Gao’s papers on this subject. They may not necessarily agree with his points of view, but these questions can serve as a good starting point and motivation for someone with a solid mechanics background and a serious interest in mechanics of biological systems. Gao believes that a complete analysis of these questions taking into account the full biological complexities requires collaborative effort of a whole community. In the published papers by Gao and coworkers, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture certainly provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. Gao’s analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. For example, the staggered nanostructure of bone is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. To understand the question on structural hierarchy, Gao proposed a “fractal bone” model with multiple levels of self-similar “hard-soft” composite structures mimicking the nanostructure of bone. The theoretically constructed fractal bone is a truly hierarchical material with different properties at different length scales and can be designed to tolerate crack-like flaws at multiple length scales.
With similar philosophy, Gao and coworkers have also been conducting research on the hierarchical biomechanics of adhesion structures of gecko. Gecko and many insects have evolved specialized adhesive tissues with bottom-up designed hierarchical structures that allow them to maneuver on vertical walls and ceilings. The adhesion mechanisms of gecko must be robust enough to function on unknown rough surfaces and also easily releasable upon animal movement. How does nature design such macroscopic sized robust and releasable adhesion devices? How can an adhesion system designed for robust attachment simultaneously allow easy detachment? These questions have motivated Gao to develop a mechanics theory of robust and releasable adhesion in biology. On the question of robust adhesion, Gao introduces a fractal gecko hairs model, somewhat similar to his fractal bone model, with self-similar fibrillar structures at multiple hierarchical levels. Gao and coworkers have shown that structural hierarchy again plays a key role in robust adhesion: it allows the work of adhesion to be exponentially enhanced with each added level of hierarchy. Gao shows that, barring fiber fracture, the fractal gecko hairs can be designed from nanoscale and up to achieve flaw tolerant adhesion at any length scales. However, consideration of crack-like flaws in the hairs themselves results in an upper size limit for flaw tolerant design. On the question of releasable adhesion, Gao has shown that the asymmetrically aligned seta hairs of gecko form a strongly anisotropic material with adhesion strength strongly varying with the direction of pulling. This orientation-dependent pull-off force enables robust attachment in the stiff direction of the material to be released by pulling in the soft direction. This strategy, which Gao succinctly termed as a “stiff-adhere, soft-release” principle, can be understood in a simple way as follows. When pulled in the stiff direction, less elastic energy can be stored in the material (much like a stiff spring can store less energy compared to a soft spring), leading to lower energy release rate to drive random crack-like flaws induced by surface roughness. On the other hand, much more elastic energy can be stored in the material when pulled in the soft direction, especially when the material is strongly anisotropic, leading to much higher energy release rate to drive the roughness induced crack-like flaws.