Measurement of shear elasticity of granular solid

Using a direct shear-box capable of very low shearing rate, we measure the force-displacement curve of cyclic, large-amplitude shear, and also the total plastic displacement residual after each cycle, for samples of glass beads. As the shear rate decreases, we observe a transition from normal, elastoplastic behavior to pure elastic behavior, with reducing residual, or total plastic, displacement after each cycle. Remarkably, this transition is also observed for large amplitude of the cyclic shear, up to 90% of the failure value. The force-displacement relation is necessarily rate-dependent during this transition. These experimental results demonstrate that granular solids may respond in a purely elastic manner, both for low amplitude force oscillations of high frequencies (such as sound) and for large amplitude ones of low frequencies, implying that the granular matter has a purely elastic regime, in which the theory of elasticity holds fully true. This regime has been overlooked in the literature, probably because its deformation rate is nearly two orders of magnitude lower than those typically used. Theoretically, the present measurements support granular solid hydrodynamics, or the fact that strong deviation from elastoplastic dynamics and rate independence take place in the low frequency limit, with a rate-dependent transition to the classic theory of elasticity.