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

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. The modelling of the biological growth is a promising bias of the contemporary mechanics of continuous media, which is connected with tissue engineering and manufacturing the novel types of composites for biomedical and technical applications. Biological tissues can be considered as multiphase continuous media composed of a solid porous skeleton (cellular walls, membranes, extracellular substances, conducting vessels) filled with liquids (intracellular, interstitial and delivering fluids). The delivering fluids contain dissolved substances that can be absorbed by a solid phase providing the mass increase of a growing body due to increase in the volume (surface or volumetric growth) and decrease in porosity