The mechanics of growth and residual stress in biological cylinders - O'Keeffe, S (2015)
Biological tissue differs from other materials in many ways. Perhaps the most crucial difference is its ability to grow. Growth processes may give rise to stresses that exist in a body in the absence of applied loads and these are known as residual stresses. Residual stress is present in many biological systems and can have important consequences on the mechanical response of a body. Mathematical models of biological structures must therefore be able to capture accurately the effects of differential growth and residual stress, since greater understanding of the roles of these phenomena may have applications in many fields. In addition to residual stresses, biological structures often have a complex morphology. The theory of 3-D elasticity is analytically tractable in modelling mechanical properties in simple geometries such as a cylinder. On the other hand, rod theory is well-suited for geometrically-complex deformations, but is unable to account for residual stress. In this thesis, we aim to develop a map between the two frameworks. Firstly, we use 3-D elasticity to determine effective mechanical properties of a growing cylinder and map them into an effective rod. Secondly, we consider a growing filament embedded in an elastic foundation. Here, we estimate the degree of transverse reinforcement the foundation confers on the filament in terms of its material properties. Finally, to gain a greater understanding of the role of residual stress in biological structures, we consider a case study: the chameleon's tongue. In particular we consider the role of residual stress and anisotropy in aiding the rapid projection of the tongue during prey capture. We construct a mechanical model of the tongue and use it to investigate a proposed mechanism of projection by means of an energy balance argument.