  Glasses exhibit a liquid-like structure but a solid-like rheological response
with plastic deformations only occurring beyond yielding. Thus, predicting the
rheological behavior from the microscopic structure is difficult, but important
for materials science. Here, we consider colloidal suspensions and propose to
supplement the static structural information with the local dynamics, namely
the rearrangement and breaking of the cage of neighbors. This is quantified by
the mean squared nonaffine displacement and the number of particles that remain
nearest neighbors for a long time, i.e. long-lived neighbors, respectively.
Both quantities are followed under shear using confocal microscopy and are the
basis to calculate the affine and nonaffine contributions to the elastic
stress, which is complemented by the viscous stress to give the total stress.
During start-up of shear, the model predicts three transient regimes that
result from the interplay of affine, nonaffine and viscous contributions. Our
prediction quantitatively agrees with rheological data and their dependencies
on volume fraction and shear rate.
