ESTONIAN ACADEMY
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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

Load transfer from the growing fibre into the growing medium: application to plant leaf growth; 162–169

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Author
Natalya Kizilova

Abstract
Biological materials change their mass, shape, and porosity during the growth and possess high strength and durability at general lightweight design. Biological tissues are considered to be inhomogeneous anisotropic multiphase composites reinforced by fibres. A 2D problem of the load transfer from the growing fibre into the growing plate with different own growth rates and viscosity is considered in this paper. Rheology of the growing biological tissue is described by a modified Maxwell model of viscoelastic media. Numerical calculations of the growth velocity and stress fields are carried out. The influence of rheological parameters of two media on the stress–strain state is investigated. It is shown that the stress field may provide local coordinated growth of the fibres and the plate when the rheological parameters of two materials are different and anisotropic growth is observed.
References
  1. Belousov, L. V. and Stein, A. A. (eds). Mechanics of Growth and Morphogenesis. Modern Problems of Biomechanics, Vol. 10. Moscow University Press, Moscow, 2002.

   2. Cowin, S. C. Strain or deformation rate dependent finite growth in soft tissues. J. Biomech., 1996, 29, 647–649.

doi:10.1016/0021-9290(95)00114-X

  3. Schopfer, P. Biomechanics of plant growth. Amer. J. Botany, 2006, 93, 1415–1425.

  4. Cosgrove, D. J. Wall relaxation and the driving forces for cell expansive growth. Plant Physiol., 1987, 84, 561–564.

  5. Entov, V. M. Mechanical model of scoliosis. J. Mech. Solids, 1983, 18, 199–206.

  6. Stein, A. A. Deformation of the rod from the growing biological material at longitudinal compression. Appl. Math. Mech., 1998, 59, 149–157.

  7. Kantor, B. Ya. and Kizilova, N. N. Mechanics of growing biological continuum. Proc. Nat. Acad. Sci. Ukraine, 2003, 2, 56–60.

  8. Kantor, B. Ya. and Kizilova, N. N. Stress-strain state investigation in bidimensional growing biological material at growth restrictions. Kharkov Nat. Univ. Vestnik, 2003, 582, 107–120.

  9. Stein, A. A. and Logvenkov, S. A. Space self-organization of a thin layer of the biological material growing on the substrate. Rep. Russian Acad. Sci., 1993, 328, 443–446.

10. Kizilova, N. N. and Egorova, E. S. Modelling of laminated growing biological materials. J. Mech. Eng., 2005, 56, 330–342.

11. Kizilova, N. N. Computational approach to optimal transport network construction in biomechanics. Lect. Notes in Computer Sci., 2004, 3044, 476–485.

12. Kizilova, N. N. Hydraulic properties of branching pipelines with permeable walls. Int. J. Fluid Mech. Res., 2005, 32, 98–109.

doi:10.1615/InterJFluidMechRes.v32.i1.60

13. Kizilova, N. N. Construction principles and control over transport systems organization in biological tissues. In Physics and Control International Conference Proceedings. IEEE Computer Society, Washington, 2003, 1, 303–308.

14. Kizilova, N. N. and Kravchenko, H. P. Investigation of stress-strain state of the 2D growing media. Mech. Solid Body, 2003, 33, 158–168.

15. Maugin, G. A. and Imatani, S. Anisotropic growth of materials. J. Physique IV (Proceedings), 2003, 105, 365–372.

16. Menzel, A. Modelling of anisotropic growth in biological tissues. Biomechan. Model. Mechanobiol., 2005, 3, 147–171.

doi:10.1007/s10237-004-0047-6

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