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Research Papers

Hierarchical Structure Enhances and Tunes the Damping Behavior of Load-Bearing Biological Materials

[+] Author and Article Information
Mahan Qwamizadeh

School of Mechanical and
Aerospace Engineering,
Nanyang Technological University,
Singapore 639798, Singapore;
Institute of High Performance Computing,
A*STAR,
Singapore 138632, Singapore

Pan Liu

School of Civil Engineering,
Wuhan University,
Wuhan, Hubei 430072, China

Zuoqi Zhang

School of Civil Engineering,
Wuhan University,
Wuhan, Hubei 430072, China;
Key Laboratory of Geotechnical and Structural
Engineering Safety of Hubei Province,
Wuhan University,
Wuhan, Hubei 430072, China;
State Key Laboratory of Water Resources
and Hydropower Engineering Science,
Wuhan University,
Wuhan, Hubei 430072, China
e-mail: zhang_zuoqi@whu.edu.cn

Kun Zhou

School of Mechanical and
Aerospace Engineering,
Nanyang Technological University,
Singapore 639798, Singapore
e-mail: kzhou@ntu.edu.sg

Yong Wei Zhang

Institute of High Performance Computing,
A*STAR,
Singapore 138632, Singapore

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 31, 2016; final manuscript received February 23, 2016; published online March 10, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051009 (Mar 10, 2016) (9 pages) Paper No: JAM-16-1062; doi: 10.1115/1.4032861 History: Received January 31, 2016; Revised February 23, 2016

One of the most crucial functionalities of load-bearing biological materials such as shell and bone is to protect their interior organs from damage and fracture arising from external dynamic impacts. However, how this class of materials effectively damp stress waves traveling through their structure is still largely unknown. With a self-similar hierarchical model, a theoretical approach was established to investigate the damping properties of load-bearing biological materials in relation to the biopolymer viscous characteristics, the loading frequency, the geometrical parameters of reinforcements, as well as the hierarchy number. It was found that the damping behavior originates from the viscous characteristics of the organic (biopolymer) constituents and is greatly tuned and enhanced by the staggered and hierarchical organization of the organic and inorganic constituents. For verification purpose, numerical experiments via finite-element method (FEM) have also been conducted and shown results consistent with the theoretical predictions. Furthermore, the results suggest that for the self-similar hierarchical design, there is an optimal aspect ratio of reinforcements for a specific loading frequency and a peak loading frequency for a specific aspect ratio of reinforcements, at which the damping capacity of the composite is maximized. Our findings not only add valuable insights into the stress wave damping mechanisms of load-bearing biological materials, but also provide useful guidelines for designing bioinspired synthetic composites for protective applications.

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Figures

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Fig. 1

The self-similar hierarchical model for typical load-bearing biological materials

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Fig. 2

Theoretical and FEM results for the variation of the storage modulus (a) and the loss modulus (b) with the aspect ratio of the mineral platelet in the single-level staggered composite (N=1) at oscillatory loadings of low frequency (f = 1 Hz) and high frequency (f = 200 Hz)

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Fig. 3

Storage (a) and loss (b) modulus of the self-similar hierarchical composites with different hierarchy number N in response to an oscillatory loading of relatively low frequency (f = 1 Hz)

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Fig. 4

(a) The storage and loss shear modulus of the homogenous protein against the loading frequency and (b) the plots of storage and loss modulus of the single-level staggered composite with respect to the loading frequency, in comparison with the data points from FEM simulations

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Fig. 5

Comparison of the storage (a) and loss modulus (b) of the self-similar hierarchical composites with different hierarchy number N

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Fig. 6

Effects of the characteristic relaxation time of protein on the storage (a) and loss modulus (b) of the homogeneous protein and its effects on the storage (c) and loss modulus (d) of the single-level staggered composite (hierarchy number N=1 and reinforcement aspect ratio ρ=100)

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Fig. 7

Effects of the protein viscous ratio on the storage (a) and loss modulus (b) of the homogeneous protein and its effects on the storage (c) and loss modulus (d) of the single-level staggered composite (hierarchy number N=1 and reinforcement aspect ratio ρ=100)

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Fig. 8

Contour plots of the storage (a) and loss modulus (b) for the single-level staggered composites versus varying loading frequency and reinforcement aspect ratio

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Fig. 9

Plots of the loss modulus for the self-similar hierarchical structure of (a) shell (hierarchy number N = 3 and mineral volume fraction φ=0.95), (b) bone (N = 7 and φ=0.45), and (c) mineralized tendon (N = 6 and φ=0.15)

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