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Bioinspired, mechanical, deterministic fractal model for hierarchical suture joints

Yaning Li, Christine Ortiz, and Mary C. Boyce
Phys. Rev. E 85, 031901 – Published 1 March 2012
Physics logo See Synopsis: Fractal Teeth

Abstract

Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies (N) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints.

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  • Received 3 September 2011

DOI:https://doi.org/10.1103/PhysRevE.85.031901

©2012 American Physical Society

Synopsis

Key Image

Fractal Teeth

Published 1 March 2012

Theoretical models show fractal hierarchical teeth can make joints stronger and more fail-resistant.

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Authors & Affiliations

Yaning Li1,2, Christine Ortiz1, and Mary C. Boyce2,*

  • 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *mcboyce@mit.edu

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Issue

Vol. 85, Iss. 3 — March 2012

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