Yielding and Rheology of vibrated beam-driven granular matter: Hysteresis and Memory

Dense granular matter has attracted significant attention due to its intricate yielding and rheological phenomena. However, unlike sheared or shaken granular systems where energy is injected at the boundaries, the yielding transition induced by vibrated beams has been rarely explored, despite its immense applications in animal and robotic locomotion on sand and underground structural engineering. In this study, we systematically vary the frequency and amplitude of beam vibration to experimentally and computationally investigate the relaxation dynamics of the granular medium. Evidence of ductile yielding behaviors with hysteresis in the frequency domain is presented. Consistency in the dynamic behaviors of both the beam and granular materials has been demonstrated. Through an analysis of mesostructural evolution, including particle motion and mechanical stability, we reveal that the hysteresis originates from anomalous diffusion induced by memory effects. A nonmonotonic constitutive law is proposed through the qualification of memory effects. This study offers insights for theoretical models of vibrated beam-driven flow, emphasizing the distinctive frequency-dependent properties through the bidirectional coupling of elastomer and granular matter.