Contact stress decomposition in large amplitude oscillatory shear of concentrated noncolloidal suspensions

The concentrated noncolloidal suspensions show complex rheological behavior, which is related to the existence of contact stress. However, determining the contact stress in time-varying flow like oscillatory shear is challenging. Herein, we propose a contact stress decomposition method to decompose the total stress directly into contact stress and hydrodynamic stress in large amplitude oscillatory shear (LAOS). The results of hydrodynamic stress and contact stress are consistent with those determined by the shear reversal experiment. The contact stress decomposition also explains the failure of the Cox-Merz rule in noncolloidal suspensions because the particle contacts exist in steady shear but are absent in small amplitude oscillatory shear. The intracycle and intercycle of contact stress are further analyzed through the general geometric average method. The intracycle behaviors exhibit strain hardening, strain softening, and shear thickening. The intercycle behaviors show bifurcations in stress-strain and stress-strain rate relations, where the transition strains at different concentrations define the state boundaries between the discrete particle contacts, the growing of particle contacts, and the saturated contacts. We also established a phenomenological constitutive model using a structural parameter to describe the shear effect on the buildup and breakdown of particle contacts. The contact stress of noncolloidal suspensions with wide ranges of particle concentrations and strain amplitudes under LAOS can be well described by the model.