Research Papers

Elastic Bounds of Bioinspired Nanocomposites

[+] Author and Article Information
H. J. Lei, B. Liu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084,China

Z. Q. Zhang

Institute of High Performance Computing,
Singapore 138632, Singapore
e-mail: zhangzq@ihpc.a-star.edu.sg

F. Han

Department of Engineering Mechanics,
School of Science,
Wuhan University of Science and Technology,
Wuhan 430065, China

Y.-W. Zhang

Institute of High Performance Computing,
Singapore 138632,Singapore

H. J. Gao

School of Engineering,
Brown University,
Providence, RI 02912

1Corresponding author.

Manuscript received December 22, 2012; final manuscript received January 22, 2013; accepted manuscript posted March 7, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061017 (Aug 21, 2013) (6 pages) Paper No: JAM-12-1568; doi: 10.1115/1.4023976 History: Received December 22, 2012; Revised January 22, 2013; Accepted March 07, 2013

Biological materials in nature serve as a valuable source of inspiration for developing novel synthetic materials with extraordinary properties or functions. Much effort to date has been directed toward fabricating and understanding bio-inspired nanocomposites with internal architectures mimicking those of nacre and collagen fibril. Here we establish simple and explicit analytical solutions for both upper and lower bounds of the elastic properties of biocomposites in terms of various physical and geometrical parameters including volume fraction and moduli of constituents, and aspect ratio and alignment pattern of stiff reinforcements. Numerical analyses based on the finite element method are performed to validate the derived elastic bounds.

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Grahic Jump Location
Fig. 1

Typical staggered nanostructures observed in load-bearing biological materials. (a) The staggered alignment of mineral platelets in shell, also referred to as the “brick-and-mortar” structure; (b) the stairwise alignment of hydroxyapatite nanocrystals in mineralized collagen fibrils of bone; (c) the “stairwise staggering” alignment of tripocollagen molecules in collagen fibrils of tendon, with a periodic unit cell comprising four tripocollagen molecules. Note that the staggered alignment of mineral crystals in bone is a result of mineralization of collagen fibrils.

Grahic Jump Location
Fig. 2

Generalized stairwise staggering alignments mimicking collagen fibrils. (a) Schematic nanostructure of biocomposites; (b) the unit cell (solid box) with staggering number n, and (c) the assumed kinematically admissible strain field under a longitudinal elongation Δ.

Grahic Jump Location
Fig. 3

(a) The assumed static equilibrium stress field in the stairwise staggered nanostructure under a longitudinal elongation Δ, (b) the distribution of shear traction along a hard platelet, and (c) the distribution of normal stress in the platelet

Grahic Jump Location
Fig. 4

The finite element mesh in a representative unit cell for (a) the regular “brick-and-mortar” structure with n = 2 and (b) a “stairwise staggering” structure with n = 5

Grahic Jump Location
Fig. 5

Variations of elastic bounds for Young's modulus as a function of the aspect ratio of platelets for (a) the “brick-and-mortar” structure with staggering number n = 2 and (b) the “stairwise staggering” structure with n = 5. In both (a) and (b), a moderate volume fraction ϕ = 50% of mineral is adopted. The dash-dotted line is the upper bound while the solid line is the lower bound. The filled square data points are from finite element analysis. The predictions from the Voigt and Mori–Tanaka models are shown as the dashed and dotted lines, respectively.

Grahic Jump Location
Fig. 6

Variation of elastic bounds for Young's modulus as a function of the aspect ratio of platelets for (a) the “brick-and-mortar” structure with staggering number n = 2 and (b) the “stairwise staggering” structure with n = 5. A large volume fraction ϕ = 90% of mineral is adopted. The dash-dotted line is the upper bound while the solid line is the lower bound. The filled square data points are from finite element analysis. The predictions from the Voigt and Mori–Tanaka models are shown as the dashed and dotted lines, respectively.




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