Stress dynamics of a 2D dense granular system near shear jamming

We study the dynamics of pressure and shear stress in a frictional 2D dense granular system using a novel apparatus that can provide fixed-volume shear without generating inhomogeneities. Under increasing shear strain, the system's pressure shows a strong increase with strain, characterized by a ``Reynolds coefficient,'' $R = d^2 P / d \gamma ^2$. R depends only on packing fraction $\phi$, and shows a strong increase as $\phi$ approaches $\phi_J$ from below. In the meantime, the system's shear stress shows a non-monotonic behavior with increasing strain. It first increases with strain as the system is in ``fragile'' states and builds up long force chains along the compression direction. After a certain amount of strain, force chains along the dilation direction starts to build up, and the system transfers into a ``shear-jammed'' state and the shear stress starts to decrease with strain. Under oscillatory shear, both pressure and shear stress show limit-cycle behavior and reach steady states after many cycles. However, the limit cycles of pressure and shear stress are very different: the pressure exhibits a hysteresis-free parabolic curve, while the shear stress exhibits a strongly hysteretic loop.