Available models of dynamic recrystallization have a number of disadvantages that in most cases make them inapplicable for practical predictions of material microstructure evolution. Both the microstructural and the empirically based approaches do not reflect physical processes leading to evolution of material defect structure in the process of plastic deformation. This work presents an attempt to develop a consistent physically-based model of dynamic recrystallization. This model, accounting for physical nature of processes of material defect structure evolution, should provide a possibility to predict evolution of several different experimentally measurable parameters of material microstructure without introduction of big number of fitting parameters. It is suggested that such a model should be based on equation for evolution of fraction of high-angle grain boundaries (HAGBs) in the process of deformation. It is shown, that the new model gives a possibility to predict the evolution of dislocation cells and grain boundaries in copper-based alloys providing good coincidence with experimental observations. Full 3-dimensional numerical simulation of multidirectional forging of copper is performed utilizing the developed dynamic recrystallization model. The same 3D simulations demonstrate new noteworthy effects connected to inhomogeneous distribution of plastic strain within the bulk of the material and material strain hardening.