Small Strain Growth and the Human Nail

The modelling framework of mass-growth developed in Soldatos (Mech. Res. Commun. 50:50–57, 2013 ; 65:35–42, 2015 ; 70:63–71, 2015 ) is specialised to describe growth processes in which mass-growth may take place elastically at infinitesimally small strain. Growth-strain is considered infinitesimally small but the resulting simplified constitutive equations are in general still non-linear due to combined action of the rate of mass-growth and the rate of volumetric strain. Nevertheless, mass-growth processes which are either incompressible or slightly/moderately compressible are found consistent with linearly elastic material behaviour, and can accordingly be studied with convenient use of linear elasticity concepts. In a relevant example application, combination of the concept of periodically accumulated small strain with a certain nail-elongation criterion enables development of a relatively simple mathematical model of the human nail apparatus and, hence, an interesting interpretation of the nail elongation process. The efficiency of the model is demonstrated through a relevant analytical solution obtained in the particular case that mass-growth in the living part of the nail takes place under constant mass density and is, therefore, incompressible. Consideration of more advanced nail features and physical concepts can be handled in a similar manner, at the expense of parts of the pursued and desirable analytical simplicity.