A microscopic theory of an equation of thixotropy from the dynamics of stress distributions in soft particle glasses.

The jammed suspensions of soft particle glasses (SPGs) exhibit interesting rheological response under start-up shear flow. Macroscopic measurements indicate SPGs "remember" their past history. We hypothesize that the rheology of SPGs is sensitive to the applied shear rate and shear history which manifest in the different microscopic rearrangements of individual particles and their contribution to the total stress. Using large scale 3D numerical simulations of model SPGs, we show that shear induced microstructural rearrangements at different points in the stress-strain curve result in distinct distributions of local stresses, which impact the overall rheological response. Interestingly, suspensions with the same microscopic stress can have very different distributions of stress locally. Although distributions of stresses vary locally, long-ranged correlations are not observed. We demonstrate that the evolution of stress distribution under start-up flow leads to the equation of thixotropy which can predict the rheological response and recover the macroscopic rheological measurements.