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Oscillatory shear has been widely used to study the rheological properties ofsuspensions under unsteady shear. Furthermore, recent works have shown thatoscillatory flows can improve the flowability of dense suspensions. While moststudies have been done under constant volume we here study oscillatory shearflows of a two-dimensional suspensions using a normal pressure-controlledset-up. To characterise the rheology, we introduce both a complex macroscopicfriction coefficient $\mu^{*}$, following the convention of the complexviscosity $\eta^{*}$, and a shear-rate averaged viscous number $J'$. Therheology and microstructure of dense suspensions are studied by systematicallyvarying both the strain magnitude $\gamma_0$ and $J'$ using numericalsimulations. We study both suspensions composed of frictional ($\mu_p=0.4$) orfrictionless ($\mu_p=0$) particles and find that the critical values, as $J'\to 0$, of both the complex macroscopic friction and the number of contacts,both total and sliding, decrease with decreasing $\gamma_0$. For suspensionscomposed of frictional particles we also find that the critical (i.e.~the shearjamming) packing fraction $\phi_c$ increase with decreasing $\gamma_0$. In bothcases, frictional and frictionless, we find that the rheological responseapproaching the shear jamming turns from a viscous to an elastic response as$\gamma_0$ is lowered below $\sim0.33$.

Oscillatory shear flows of dense suspensions at imposed pressure: Rheology and micro-structure