Mass-growth of a finite tube reinforced by a pair of helical fibres

Soldatos, Kostas P.

Abstract

Several types of tube-like fibre-reinforced tissue, including the layers of arteries and veins, different kinds of muscle, biological tubes as well as plants and trees, are reinforced by a pair of helical fibres wound symmetrically around the tube axis in opposite directions. In many cases, this kind of biological structures grow in an axially symmetric manner that preserves their own shape as well as the direction and shape of their embedded pair of helical fibres. This study considers and investigates the influence that preservation of fibre direction exerts on pseudo-elastic (elastic-like) mass-growth modelling of the described fibre-reinforced structure. Complete sets of necessary conditions that enable the implied axisymmetric tube mass-growth to take place are sought, found and presented. These hold in addition to, and simultaneously with standard kinematic relations and equilibrium equations met in conventional hyperelasticity. They thus render this mass-growth mathematical model the properties of an apparently overdetermined boundary value problem. However, the additional information they provide leads to identification of admissible classes of strain energy densities for growth that enable realisation of the implied type of tube mass-growth. The analysis is applicable to several different types of mass-growth of tube-like tissue reinforced by a pair of symmetrically wound helical fibres. This is demonstrated with an application which considers that mass-growth of the fibre-reinforced tube takes place in an incompressible manner; namely, in a non-isochoric manner that along with fibre direction, it also preserves the material density of the growing tube.

Citation

Soldatos, K. P. (2019). Mass-growth of a finite tube reinforced by a pair of helical fibres. Mechanics Research Communications, 95, 71-78. https://doi.org/10.1016/j.mechrescom.2019.01.002

• Journal Article Type: Article
• Acceptance Date: Jan 3, 2019
• Online Publication Date: Jan 7, 2019
• Publication Date: Jan 7, 2019
• Deposit Date: Jan 8, 2019
• Publicly Available Date: Jan 8, 2020
• Journal: Mechanics Research Communications
• Print ISSN: 0093-6413
• Electronic ISSN: 1873-3972
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Pages: 71-78
• DOI: https://doi.org/10.1016/j.mechrescom.2019.01.002
• Keywords: Anisotropic mass-growth; Elastic-like mass-growth; Growth of cylinders and tubes; Helical fibres; Mass-growth modelling; Pseudo-elastic mass-growth
• Public URL: https://nottingham-repository.worktribe.com/output/1450498
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0093641318304828
• Additional Information: This article is maintained by: Elsevier; Article Title: Mass-growth of a finite tube reinforced by a pair of helical fibres; Journal Title: Mechanics Research Communications; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.mechrescom.2019.01.002; Content Type: article; Copyright: © 2019 Elsevier Ltd. All rights reserved.