Relaxation and rheology in beam-vibrated granular system

The yielding transition in dense granular matter under vibrated beams, despite its significance for animal and robotic locomotion on granular surfaces and underground structural engineering, remains underexplored. In this study, we systematically modulate the frequency and amplitude of beam vibrations through experiments and simulations to investigate the granular relaxation dynamics. We uncover dual yielding behaviors: gradual, ductile transitions in the time domain, where the system smoothly stabilizes, and abrupt, brittle transitions in the frequency domain, characterized by sharp shifts between metastable states and pronounced hysteresis, highlighting the dynamic consistency between the behavior of the beam and the granular materials. Through detailed analysis of the mesostructural evolution, encompassing particle motion, and mechanical stability, we unveil the root of the hysteresis as stemming from anomalous diffusion driven by memory effects, where the system's response is influenced by its stress history. These findings lead to the development of a nonmonotonic constitutive law that captures the unique frequency-dependent coupling between the beam and granular material. Our findings pave the way for advanced theoretical models in this domain, offering profound insights into the nuanced behaviors of vibrated granular systems.