Shock wave due to the short-period impact in one-dimensional plasticity bead chain

The waves in a one-dimensional (1-D) bead chain produced by a constant velocity impact in a short period are studied numerically in the present paper. It seems that in some cases, the waves look like a shock wave, while in other cases they may be composed of several solitary waves or some oscillations. These characteristics depend on both the bead parameters and the impact parameters, such as the plasticity of the bead material, the piston velocity and the impact duration. It is found that the shock structure appears if the duration of the impact is longer, while it will evolve into several solitary waves if the duration of the impact is small enough. This indicates that the bead velocity attenuates with power function. The strength of the attenuation depends on the plasticity, the piston velocity and the bead radius.