Dynamic hairspray analysis. III. Theoretical considerations.

Abstract

Model mechanical calculations were carried out to simulate the properties of hair fiber assemblies operating in the bending mode. It was assumed that the fibers were in omega-loop configuration (as in experimental work), and the theory of deformation of thin rings provided a fundamental relationship between stress and strain. A dependence on the stiffness of multi-fiber assembly was derived and verified empirically. Theoretical bending stiffness for fixative-treated hair was calculated for various model fiber distributions by calculating their area moment of inertia according to the parallel axis theorem. General equations for stiffness of fiber assemblies were derived for cross sections placed on cubic and hexagonal lattices. The results suggest a good agreement between the theoretical and experimental data.