Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Mechanics of Fibrous Biological Materials With Hierarchical Chirality J. Appl. Mech. 2016;83(10):101010-101010-7. doi:10.1115/1.4034225 Figure Legend: The formed twisted belts of fully deswelled paper sheets