管腔结构软组织的三维形貌失稳

谢伟华; 尹思凡; 李博; 曹艳平; 冯西桥

doi:10.7498/aps.65.188704

摘要

生物软组织生长失稳的研究，有助于理解生物组织各种形貌的形成机制，并为某些疾病的诊断和治疗提供参考. 本文基于连续介质力学方法，利用体生长模型和增量变形理论，分析了圆柱状生物软组织的三维形貌失稳. 结果表明，在圆柱外边界自由时，系统可能出现三种失稳形式-欧拉失稳、轴对称失稳和四方失稳；而当圆柱外边界固定时，系统可以发生轴对称失稳和四方失稳. 通过有限元模拟，给出了在上述两种边界条件下圆柱状生物软组织失稳形貌的相图. 进而采用伪动力学方法，研究了形貌的后屈曲演化特征.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
清华大学工程力学系, 北京 100084

通信作者: 冯西桥, fengxq@tsinghua.edu.cn

基金项目: 国家自然科学基金（批准号：11432008，11542005）资助的课题.

Authors and contacts

1.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Corresponding author: Feng Xi-Qiao, fengxq@tsinghua.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11432008, 11542005).

参考文献

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[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

施引文献

[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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