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Research Papers

Buckling Behaviors of Staggered Nanostructure of Biological Materials

[+] Author and Article Information
Zhiling Bai

Biomechanics and Biomaterials Laboratory,
Department of Applied Mechanics,
Beijing Institute of Technology,
Beijing 100081, China

Yewang Su

State Key Laboratory of Nonlinear Mechanics,
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: yewangsu@imech.ac.cn

Baohua Ji

Biomechanics and Biomaterials Laboratory,
Department of Applied Mechanics,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: bhji@bit.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 1, 2015; final manuscript received November 27, 2015; published online December 16, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(3), 031011 (Dec 16, 2015) (9 pages) Paper No: JAM-15-1586; doi: 10.1115/1.4032116 History: Received November 01, 2015; Revised November 27, 2015

The nanostructure of biological materials is built with hard mineral crystals embedded in soft protein matrix in a staggered manner. The staggered arrangement of the crystals is assumed to be critically important for the stability of the nanostructure. But the mechanism is not fully understood. In this paper, a mechanical model, considering the effects of overlapping ratio between the crystals, i.e., the staggering position, is developed for analyzing the buckling behaviors of the nanostructure. It is found that the buckling strength increases with the overlapping ratio λ in the range of 0–1/2 and reaches a peak value at λ = 1/2 that is generally adopted by nature's design of the biological materials. The effect of aspect ratio and volume fraction of mineral crystals are further analyzed at various overlapping ratios, and the results are in general consistent with previous studies for the case of λ = 1/2. In addition, the lower and upper limits of the buckling strength are obtained. Finally, we show that the contact between mineral tips can significantly enhance the buckling strength of the nanostructure when the aspect ratio of minerals is small.

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Figures

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Fig. 4

Free-body diagrams of elements of (a) protein matrix and (b) mineral crystal

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Fig. 3

The normalized tensile and compressive modulus of the nanostructure. The normalized moduli versus aspect ratio for (a) bone (Vm=45%), (b) nacre (Vm=95%), and (c) the normalized moduli versus the volume fraction of mineral crystals.

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Fig. 2

The model of nanostructure of biological materials under compression. (a) Illustration of the nanostructure where the mineral crystals staggered in the protein matrix with an overlapping length Ls. An RVE is line out by a dashed rectangle, (b) partition of the RVE into four parts, denoted by I, II, III, and IV, and (c) two special cases of the staggered arrangement: λ=0,1 and λ=1/2.

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Fig. 1

Typical biological materials and their nanostructures. The images of (a) bone tissue, (b) nacre, and (c) schematic illustration of the nanostructure consisting of hard mineral crystals embedded in soft protein matrix in a staggered manner.

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Fig. 5

The effect of overlapping ratio λ on the normalized buckling strength of the nanostructure σ¯c in the case of Vm=45% and ρ=10

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Fig. 6

The predicted buckling modes of the nanostructure changing with the aspect ratio and overlapping ratio

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Fig. 7

The effect of overlapping ratio λ and aspect ratio ρ on the buckling strength σ¯c for (a) bone (Vm=45%) and (b) nacre (Vm=95%)

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Fig. 8

The effect of volume fraction of mineral crystals on the buckling strength for (a) ρ=5, (b) ρ=10, and (c) ρ=20

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Fig. 9

The buckling strength predicted by the present study with tip-pinned model in comparison with that of previous study with tip-free model at various aspect ratios and volume fraction: (a) Vm=45% for bone and (b) Vm=95% for nacre

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Fig. 10

The buckling modes predicted by the present study with tip-pinned model and in comparison with that of previous study with tip-free model at various aspect ratios

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