Family of plane solitary waves in dimer granular crystals.

Uniform planar impact on a two-dimensional square packing of spheres with intruders at interstitial locations is investigated. An equivalent one-dimensional granular chain model is proposed with appropriate scaling and is verified numerically. Numerical observations demonstrate the existence of a new family of plane solitary waves with different profiles at unique combinations of material properties. In particular, a special case of a solitary wave whose profile is similar to that of the homogeneous chains is also reported. Material combinations that cause solitary waves are systematically extracted for a wide range of material properties. For the solitary wave similar to that of a homogeneous chain, a quasicontinuum approximation is employed to predict the shape and width of the solitary wave, showing good agreement with the numerical results. Finally, an asymptotic analysis is conducted to predict the solitary wave solutions.

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.

Wave propagation in random granular chains.

The influence of randomness on wave propagation in one-dimensional chains of spherical granular media is investigated. The interaction between the elastic spheres is modeled using the classical Hertzian contact law. Randomness is introduced in the discrete model using random distributions of particle mass, Young's modulus, or radius. Of particular interest in this study is the quantification of the attenuation in the amplitude of the impulse associated with various levels of randomness: two distinct regimes of decay are observed, characterized by an exponential or a power law, respectively. The responses are normalized to represent a vast array of material parameters and impact conditions. The virial theorem is applied to investigate the transfer from potential to kinetic energy components in the system for different levels of randomness. The level of attenuation in the two decay regimes is compared for the three different sources of randomness and it is found that randomness in radius leads to the maximum rate of decay in the exponential regime of wave propagation.