Influence of Lateral Constraints on Wave Propagation in Finite Granular Crystals

In the presented work, wave dynamics of 2D finite granular crystals of polyurethane cylinders under low-velocity impact loading was investigated to gain better understanding of the influence of lateral constraints. The deformation of the individual grains in the granular crystals during the impact loading was recorded by a high-speed camera and digital image correlation (DIC) was used to calculate high fidelity kinematic and strain fields in each grain. These grain-scale kinematic and strain fields were utilized for the computation of the intergranular forces at each contact using a granular element method (GEM) based mathematical framework. Since the polyurethane were viscoelastic in nature, the viscoelasticity constitutive law was implemented in the GEM framework and it was shown that linear elasticity using the strain rate-dependent coefficient of elasticity is sufficient to use instead of a viscoelastic framework. These particle-scale kinematic and strain field measurements in conjunction with the interparticle forces also provided some interesting insight into the directional dependence of the wave scattering and attenuation in finite granular crystals. The directional nature of the wave propagation resulted in strong wave reflection from the walls. It was also noteworthy that the two reflected waves from the two opposite sidewalls result in destructive interference. These lateral constraints at different depths leads to significant differences in wave attenuation characteristics and the finite granular crystals can be divided into two regions: upper region, with exponential wave decay rate, and lower region, with higher decay rate.