Application of non-linear strain waves to the study of the growth of long bones

A non-linear dynamic model is developed to account for material inhomogeneities in a growth plate in long bones. The governing equations are obtained to account for non-linear dispersive, viscoelastic and inhomogeneous features of the growth plate. The evolution of non-linear strain waves over the material inhomogeneities is obtained via the asymptotic solutions. It is shown that variations in the amplitude and the width of both the bell-shaped and kink-shaped waves reflect the position and the size of the inhomogeneity. This may be used for a detection of the growing plate features and in the development of the reaction–diffusion equation for the stimulus of the growth of long bones.