Characterization of wave propagation in elastic and elastoplastic granular chains

For short duration impulse loadings, elastic granular chains are known to support solitary waves, while elastoplastic chains have recently been shown to exhibit two force decay regimes [Pal, Awasthi, and Geubelle, Granular Matter 15, 747 (2013).]. In this work, the dynamics of monodisperse elastic and elastoplastic granular chains under a wide range of loading conditions is studied, and two distinct response regimes are identified in each of them. In elastic chains, a short loading duration leads to a single solitary wave propagating down the chain, while a long loading duration leads to the formation of a train of solitary waves. A simple model is developed to predict the peak force and wave velocity for any loading duration and amplitude. In elastoplastic chains, wave trains form even for short loading times due to a mechanism distinct from that in elastic chains. A model based on energy balance predicts the decay rate and transition point between the two decay regimes. For long loading durations, loading and unloading waves propagate along the chain, and a model is developed to predict the contact force and particle velocity.