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Investigations of the growth-induced deformations of soft biological tissues may help understand the underlying mechanical mechanisms of their morphogenesis and provide clues for diagnosing some diseases. In the framework of continuum mechanics, we establish a three-dimensional model to analyze the instabilities of cylindrical soft tissues induced by volumetric growth. The different three-dimensional wrinkling patterns under either free or fixed boundary conditions at the outer surface are considered. It is found that Euler buckling, axially symmetrical wrinkling, and checkerboard wrinkling may occur under the traction-free boundary conditions, while axisymmetric pattern and checkerboard pattern often appear under the fixed boundary conditions. Phase diagrams are constructed to predict the morphologies in terms of the geometrical and material parameters of the system. Besides, a pseudo-dynamic numerical method is invoked to simulate the postbuckling evolutions of the wrinkling patterns.
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Keywords:
- soft biological tissue /
- growth /
- tubular organ /
- instability
[1] Balbi V, Ciarletta P 2013 J. R. Soc. Interface 10 20130109
[2] Balbi V, Kuhl E, Ciarletta P 2015 J. Mech. Phys. Solids 78 493
[3] Li B, Cao Y P, Feng X Q, Gao H 2012 Soft Matter 8 5728
[4] Fung Y C 1991 Ann. Biomed. Eng. 19 237
[5] Goriely A, Destrade M, Ben Amar M 2006 Q. J. Mech. Appl. Math. 59 615
[6] Li B, Jia F, Cao Y P, Feng X Q, Gao H 2011 Phys. Rev. Lett. 106 234301
[7] Ben Amar M, Jia F 2013 Proc. Natl. Acad. Sci. USA 110 10525
[8] Ciarletta P, Ben Amar M 2012 J. Mech. Phys. Solids 60 525
[9] Li B, Cao Y P, Feng X Q 2011 J. Biomech. 44 182
[10] Li B, Cao Y P, Feng X Q, Gao H 2011 J. Mech. Phys. Solids 59 758
[11] Moulton D E, Goriely A 2011 J. Mech. Phys. Solids 59 525
[12] Shyer A E, Tallinen T, Nerurkar N L, Wei Z, Gil E S, Kaplan D L, Tabin C J, Mahadevan L 2013 Science 342 212
[13] Xie W H, Li B, Cao Y P, Feng X Q 2014 J. Mech. Behav. Biomed. Mater. 29 594
[14] Han H C 2008 J. Biomech. 41 2708
[15] Han H C 2009 J. Biomech. 42 2797
[16] Han H C, Chesnutt J K, Garcia J R, Liu Q, Wen Q 2013 Ann. Biomed. Eng. 41 1399
[17] Han H C, Ku D N, Vito R P 2003 Ann. Biomed. Eng. 31 403
[18] Ben Amar M, Goriely A 2005 J. Mech. Phys. Solids 53 2284
[19] Ogden R W 1997 Non-Linear Elastic Deformations (New York: Courier Dover Publications)
[20] Lee A Y, Han B, Lamm S D, Fierro C A, Han H C 2012 Am. J. Physiol. 302 H873
[21] Johnson F P 1910 Am. J. Anatomy 10 521
[22] McLin V A, Henning S J, Jamrich M 2009 Gastroenterology 136 2074
[23] Yasugi S 1993 Dev. Growth Differ. 35 1
[24] Rodriguez E K, Hoger A, McCulloch A D 1994 J. Biomech. 27 455
[25] Jia F, Li B, Cao Y P, Xie W H, Feng X Q 2015 Phys. Rev. E 91 012403
[26] Cai S, Breid D, Crosby A J, Suo Z, Hutchinson J W 2011 J. Mech. Phys. Solids 59 1094
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[1] Balbi V, Ciarletta P 2013 J. R. Soc. Interface 10 20130109
[2] Balbi V, Kuhl E, Ciarletta P 2015 J. Mech. Phys. Solids 78 493
[3] Li B, Cao Y P, Feng X Q, Gao H 2012 Soft Matter 8 5728
[4] Fung Y C 1991 Ann. Biomed. Eng. 19 237
[5] Goriely A, Destrade M, Ben Amar M 2006 Q. J. Mech. Appl. Math. 59 615
[6] Li B, Jia F, Cao Y P, Feng X Q, Gao H 2011 Phys. Rev. Lett. 106 234301
[7] Ben Amar M, Jia F 2013 Proc. Natl. Acad. Sci. USA 110 10525
[8] Ciarletta P, Ben Amar M 2012 J. Mech. Phys. Solids 60 525
[9] Li B, Cao Y P, Feng X Q 2011 J. Biomech. 44 182
[10] Li B, Cao Y P, Feng X Q, Gao H 2011 J. Mech. Phys. Solids 59 758
[11] Moulton D E, Goriely A 2011 J. Mech. Phys. Solids 59 525
[12] Shyer A E, Tallinen T, Nerurkar N L, Wei Z, Gil E S, Kaplan D L, Tabin C J, Mahadevan L 2013 Science 342 212
[13] Xie W H, Li B, Cao Y P, Feng X Q 2014 J. Mech. Behav. Biomed. Mater. 29 594
[14] Han H C 2008 J. Biomech. 41 2708
[15] Han H C 2009 J. Biomech. 42 2797
[16] Han H C, Chesnutt J K, Garcia J R, Liu Q, Wen Q 2013 Ann. Biomed. Eng. 41 1399
[17] Han H C, Ku D N, Vito R P 2003 Ann. Biomed. Eng. 31 403
[18] Ben Amar M, Goriely A 2005 J. Mech. Phys. Solids 53 2284
[19] Ogden R W 1997 Non-Linear Elastic Deformations (New York: Courier Dover Publications)
[20] Lee A Y, Han B, Lamm S D, Fierro C A, Han H C 2012 Am. J. Physiol. 302 H873
[21] Johnson F P 1910 Am. J. Anatomy 10 521
[22] McLin V A, Henning S J, Jamrich M 2009 Gastroenterology 136 2074
[23] Yasugi S 1993 Dev. Growth Differ. 35 1
[24] Rodriguez E K, Hoger A, McCulloch A D 1994 J. Biomech. 27 455
[25] Jia F, Li B, Cao Y P, Xie W H, Feng X Q 2015 Phys. Rev. E 91 012403
[26] Cai S, Breid D, Crosby A J, Suo Z, Hutchinson J W 2011 J. Mech. Phys. Solids 59 1094
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