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Research Papers

Mechanics of Fibrous Biological Materials With Hierarchical Chirality

[+] Author and Article Information
Huijuan Zhu

Department of Mechanics,
Tianjin University,
Yaguan Road No.135,
Tianjin 300054, China
e-mail: zh_huijuan@foxmail.com

Takahiro Shimada

Department of Mechanical
Engineering and Science,
Kyoto University,
Nishikyo-Ku,
Kyoto 615-8540, Japan
e-mail: shimada@me.kyoto-u.ac.jp

Jianshan Wang

Department of Mechanics,
Tianjin University,
Yaguan Road No.135,
Tianjin 300054, China
e-mail: wangjs@tju.edu.cn

Takayuki Kitamura

Department of Mechanical
Engineering and Science,
Kyoto University,
Nishikyo-Ku,
Kyoto 615-8540, Japan
e-mail: kitamura@kues.kyoto-u.ac.jp

Xiqiao Feng

CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: fengxq@tsinghua.edu.cn

1Corresponding author.

Manuscript received February 27, 2016; final manuscript received June 25, 2016; published online August 18, 2016. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 83(10), 101010 (Aug 18, 2016) (7 pages) Paper No: JAM-16-1114; doi: 10.1115/1.4034225 History: Received February 27, 2016; Revised June 25, 2016

Chirality simultaneously exists at different length scales in many biological materials, e.g., climbing tendrils and bacterial flagella. It can transfer from lower structural levels to higher structural levels, which is tightly associated with the growth and assembly of biological materials. In this paper, a continuum mechanics model is presented for understanding the bottom–up transfer of chirality in fibrous biological materials. Basic physical mechanisms underlying the chirality transfer in biological world are revealed. It is demonstrated that the chirality of constituent elements at the microscale can induce the twisting of higher-level structures, which may further transfer into the macroscopic morphology in different manners, rendering the formation of hierarchically chiral structures in tissues or organs. The bottom–up transfer mechanism of chirality may provide a limit to the macroscopic size of biological materials through the accumulative contribution of twisting.

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Figures

Grahic Jump Location
Fig. 1

Hierarchy of chirality in biological materials: (a) sugar unit, (b) cellulose molecule, (c) cellulose fibril, (d) single cell with helical winding of cellulose fibrils, (e) fiber bundle, (f) fiber network, (g) twisted belt, and (f) macroscopic helix

Grahic Jump Location
Fig. 2

Physical mechanism of intrinsic twist. (a) A fully swelled cell with the lowest value of helical angle α=α0, (b) a partially swelled cell with helical angle α=α1>α0, and (c) a fully deswelled cell with the largest helical angle α=α2>α1. During the deswelling process from (a) to (c), the helical angle of the cellulose fibril helix increases with decreasing cell wall radius. The shape changes of cellulose fibril helices induce an equivalent torque acting on the cross section of cell, which leads to the intrinsic torque acting on the cell. The directions and values of the equivalent torque are determined by the helical angle change. Furthermore, the cross-sectional radius of the cell wall is limited by cellulose winding.

Grahic Jump Location
Fig. 3

The formed twisted belts of fully deswelled paper sheets

Grahic Jump Location
Fig. 4

Variations of the twisting angle per unit length with the water content for different paper sheets. The water content is defined as X=(m2−m1)/m1×100%, where m1 and m2 are the weight of paper sheet before and after swelling, respectively.

Grahic Jump Location
Fig. 5

Variations of the twisting angle per unit length with thewidth for different paper sheets. Fitting curves: Yblack=2.484x−1.1,Yblue=2.903x−0.964 and Yred=2.904x−0.725.

Grahic Jump Location
Fig. 6

The formation of the torsion and curvature of the fibernetwork with the helical angle changes of cellulose fibrilhelices. Here, b=2 mm and κ0=1000. In the calculation, we take H=2r and the cross-sectional radius of cellulose fibrilsr=r0(1+βTΔC), where r0=2.0×10−6 m, Q11=3.798 GPa, Q22=91.37 GPa, Q12=9.154 GPa, Q33=1.2 GPa, Q44=Q55=1.008 GPa, Q66=0.998 GPa,Q12=Q23=0 GPa [28], p=1 and q=2.

Grahic Jump Location
Fig. 7

The evolution of the torsion and curvature of the fiber network with the helical angle changes of cellulose fibril helices. The helical shape variations of the fiber network with the helical angles of cellulose fibril helices at the subcellular level. We take the initial curvature κ0=125.

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