Understanding, predicting, and controlling microstructure evolution is the one of the keys to designing next generation, high performance structural materials. Microstructure evolution is mediated by the motion of grain boundaries (GBs) in response to mechanical, thermal, or internal driving forces. The wide range of GB behavior makes them difficult to quantify and model predictively. Molecular dynamics, historically the workhorse of microstructure evolution, has limited application to large problems. Mesoscale modeling of microstructure evolution is attractive due to its scalability, but often oversimplifies the complex range of GB migration behaviors. Here, we use the multiphase field method, combined with the principle of minimum dissipation potential and strongly nonconvex GB energy, to simulate boundary migration. We show that disconnections, generally accepted as the mediators of boundary migration, appear spontaneously using this framework. The method is then applied to a number of cases of interest, including shear coupling, thermal softening, and geometric hardening.