Introduction

Granular materials are widely found in nature or industrial production, and are complex systems composed of a large number of discrete solid particles (Kou et al. in Nature 551:360–363, 2017; Clerc et al. in Nat Phys 4:249–254, 2008). Granular materials have the special mechanical properties of solids or fluids, and solid–liquid-like transformation phenomena occur under certain conditions. The energy of granular systems can be dissipated rapidly by the friction and damping between particles, and the contact force and direction can be adjusted by the particle rearrangement. The local load can be extended in space and then form a stable granular system.