On elastic growth modelling of straight hair

Soldatos, Konstantinos (2017) On elastic growth modelling of straight hair. Mathematics and Mechanics of Solids . ISSN 1741-3028

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Certain macroscopic similarities of the nail and hair elongation mechanisms enable the mass-growth activity that takes place within a straight hair follicle to be modelled through a suitable extension of a relevant small-strain pseudo-elasticity model of human nail growth. Basic differences which are taken into consideration are the facts that straight hair (a) resembles the form of a cylindrical rod, rather than a plate, while (b) its material constitution seems microscopically transversely isotropic, rather than isotropic. A complete analytical solution of the obtained governing differential equations is detailed for the case where incompressible mass-growth conditions prevail within the hair matrix. In addition to estimating displacement and stress distributions that develop within the growing matrix, and the resulting hair elongation, that solution enables prediction of a clinically observed zone of hair-fibre hardening that lies between the matrix soft tissue and the hard keratinous hair shaft. It also predicts that the longitudinal dimension of the hair matrix and that of the hair-fibre hardening zone depend on the material properties of the soft tissue of the follicle. Consideration of more advanced micro- or macro-scopic features of the hair follicle, such as layered structure or curved form, can be handled mathematically in a similar manner at the expense of analytical simplicity.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/840591
Keywords: Elastic mass-growth, incompressible mass-growth, linearly elastic growth, mass-growth, small strain growth, straight hair elongation
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1177/1081286516680392
Depositing User: Eprints, Support
Date Deposited: 31 Aug 2017 08:54
Last Modified: 04 May 2020 18:30
URI: https://eprints.nottingham.ac.uk/id/eprint/45287

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