A framework for crossover of scaling law : dynamical impact of viscoelastic board

Abstract

In this paper, a crossover of scaling laws is described as a result of the interference from selfsimilar variable of the higher class of the self-similarity on the dynamical impact of solid sphere onto a viscoelastic surface. All the physical factors including the size of spheres, the impact of velocity are successfully summarized to the primal dimensionless numbers which construct a selfsimilar solution of the second kind, which represents the balance between dimensionless numbers. The self-similar solution gives two different scaling laws by the perturbation method describing the crossover. These theoretical predictions are compared with experimental results to show good agreement. It was suggested that a hierarchical structure of similarity plays a fundamental role on crossover, which offers a fundamental insight to self-similarity in general.