Dynamic analysis of contact forces in disc assemblies by the shadow method of caustics

Abstract

The shadow method of dynamic caustics was utilized to study contact force transfer in circular disc assembles under low-speed impact. Caustic mapping equations were derived to relate the caustic pattern to the stress invariant near the concentrated force on the disc, and a characteristic dimension connecting the extreme points of the caustic curve was proposed to evaluate the magnitude and direction of the resultant contact force in order to determine the normal and tangential contact components. Transient patterns of the caustic shadows were analysed for the disc assemblies of the one-dimensional column, square arrangement, and triangular arrangement. Under impulsive loads, force transmission chains were observed in the two-dimensional assemblies and their transient values were solved to represent the contact histories. The influence of impact mass and impulsive velocity was analysed on the contact forces among the discs in the column assembly to show the typical responses of the aligned particles in the granular systems.