In this study, the phase diagram of Pluronic L64 and water is simulated via dissipative particle dynamics (DPD). The peculiar structures that form when the concentration varies from dilute to dense (i.e., spherical and rod-like micelles, hexagonal and lamellar phases, as well as reverse micelles) are recognized, and predictions are found to be in good agreement with experiments. A novel clustering algorithm is used to identify the structures formed, characterize them in terms of radius of gyration and aggregation number and cluster mass distributions. Non-equilibrium simulations are also performed, in order to predict how structures are affected by shear, both via qualitative and quantitative analyses. Despite the well-known scaling problem that results in unrealistic shear rates in real units, results show that non-Newtonian behaviors can be predicted by DPD and associated with variations of the observed microstructures. Published by AIP Publishing.