Tissue tension and axial growth of cylindrical structures in plants and elastic tissuesR. Vandiver1 and A. Goriely1, 2
1 Program in Applied Mathematics, University of Arizona - Tucson, AZ 85721, USA
2 Department of Mathematics and Program in Applied Mathematics, University of Arizona - Tucson, AZ 85721, USA
received 24 June 2008; accepted in final form 28 October 2008; published December 2008
published online 12 December 2008
In many cylindrical structures in biology, residual stress fields are created through differential growth. In particular, if the outer and inner layers of a cylinder grow differentially, parts of the cylinder will be in a state of axial compression and other parts will be in tension. These tissue tensions change the overall material properties of the structure. Here, we study the role of tissue tension in the overall rigidity and stability of the cylinder. A detailed analysis, based on nonlinear elasticity, of the effect of tissue tension on the mechanical properties of growing cylinders reveal a subtle interplay between geometry, growth, and nonlinear elastic responses that help understand some of the remarkable properties of stems and other biological tissues.
87.85.gp - Mechanical systems.
46.32.+x - Static buckling and instability.
89.20.-a - Interdisciplinary applications of physics.
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