Highly nonlinear solitary waves in chains of hollow spherical particles

We study the dynamic response of one- dimensional granular chains composed of uniform hollow spheres excited by an impulse, and we observe the formation and propagation of highly nonlinear solitary waves. We find that the dynamics of these solitary waves are different from the solitary waves forming in chains composed of uniform solid spheres, because of the changes in the contact interaction between particles. We study the quasi-static contact interaction between two hollows spheres using finite element (FE) simulations, and approximate their response as a power-law type function in the range of forces of interest for this work. The experimental data obtained by testing a chain of particles shows good agreement with theoretical predictions obtained using a long wavelength approximation, and with numerical simulations based on discrete particle and FE models. We also investigate the effect of hollow spheres' wall thickness on the dynamic response of the chains.