Applied Mathematics and Mechanics

, Volume 40, Issue 12, pp 1847–1860 | Cite as

Morphology of cylindrical cell sheets with embedded contractile ring

  • Nan Nan
  • Guohui HuEmail author


The behavior of large deformations of cellular tissues is usually affected by the local properties of cells and their interactions, resulting in folding which acts as an important role in the embryonic development, as well as growing and spreading of a tumor, which can rapidly promote the stereo complexity of the architecture of the tissues. In the present study, a cylindrical vertex model is constructed to explore the morphology of the tubular cell sheets subject to an embedded contractile ring. It is found that an inner region of the contractile ring in equilibrium will protrude from the tube wall, and it will suddenly collapse when the contractile strength exceeds a threshold, indicating the occurrence of a bifurcation. These results on the effect of embedded contraction in the tubular shell are quite different from the planar cases, which can reveal the importance of the interaction between the geometric and material non-linearity in cylindrical geometry. The dependence of the large deformation on the bending modulus parameters and contraction strength is also analyzed for the cylindrical cell shell.

Key words

vertex model cylindrical cell sheet contractile ring large deformation protrusion 

Chinese Library Classification

O39 Q66 

2010 Mathematics Subject Classification

92C10 92C05 


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering ScienceShanghai UniversityShanghaiChina

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