Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear

In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in reversible phase where particle form closed loops below yielding point. When friction coefficient is small, storage modulus exhibits softening, loss remains finite quasi-static limit. As increases, softening residual are suppressed. The moduli satisfy scaling laws if they plotted as functions areas loop divided by strain amplitude diameter grains, at least for their small values.