Mechanical Principles of a Self-Similar Hierarchical Structure
- PDF / 480,256 Bytes
- 12 Pages / 612 x 792 pts (letter) Page_size
- 17 Downloads / 162 Views
1188-LL01-01
Mechanical Principles of a Self-Similar Hierarchical Structure Huajian Gao Division of Engineering, Brown University, Providence, RI, 02912, USA.
ABSTRACT Natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multiscale hierarchical structures. Here we summarize some recent studies on an idealized selfsimilar hierarchical model of bone and bone-like materials, and discuss mechanical principles of self-similar hierarchy, in particular to show how the characteristic length, aspect ratio and density at each hierarchical level can be selected to achieve flaw tolerance and superior stiffness and toughness across scale. Tel.: (401) 863-2626; Email address: [email protected]
INTRODUCTION Multi-level structural hierarchy can be observed in many biological systems including bone [1-6] and attachment pads of gecko [7-9]. In fact, structural hierarchy is a rule of nature. Hierarchical structures can be observed in all biosystems from chromosome, protein, cell, tissue, organism, to ecosystems. What are the roles and principles of structural hierarchy? What determine the size scales and other geometrical factors in a hierarchical material? These questions should be of general interest to both engineering and biological systems. Recent studies on biological materials have shown that the characteristic size at each level of structural hierarchy may have been selected to ensure tolerance of material/structural flaws. For example, it has been demonstrated [10,11] that, due to their nanoscale characteristic size, the mineral bits in bone and bone-like materials tend to fail not by propagation of preexisting cracks but by uniform rupture at the limiting strength of the material. For biological adhesion systems [7,8,12], similar transition from crack-like failure to uniform rupture has also been discussed [13]; the adhesion strength is affected not only by the size but also by the shape of the contacting surfaces: the smaller the size, the less important the shape, and shapeinsensitive optimal adhesion was found to become possible when the structural size is reduced to below a critical length around 100 nm for van der Waals adhesion [14]. In this paper, we summarize some recent studies on an idealized self-similar hierarchical model mimicking the structure of bone [6,15]. It is known that bone and bone-like materials (Fig. 1) exhibit hierarchical structures over many length scales. For example, sea shells have 2 to 3 levels of lamellar structure [1,2,16-18], while vertebral bone has 7 levels of structural hierarchy [2, 19-22] (Fig. 2). Although the higher level structures of bone and bone-like materials show great complexity and variations, they exhibit a generic nanostructure (Fig. 2) at the most elementary level of structural hierarchy Figure 1. Bone and bone-like materials. consisting of nanometer sized hard mineral
crystals arranged in a parallel staggered pattern in a soft protein matrix [3,5,10]. The nanostructure of tooth enamel shows needle-like (15–20nm thick and 1000nm
Data Loading...
