A general model of microstructure evolution including phase transformation in elasto‐plastic materials

Abstract The evolution of microstructures can be observed in various engineering and natural materials, such as special alloys, silica glasses or soils. These macroscopic and microscopic effects are often controlled by thermal and chemical changes or extern forces. In addition, several phases are usually involved in these processes, whose energy potentials result in a non‐convex total energy. A theory is introduced that can be applied to a wide range of elasto‐plastic materials with kinematic hardening. In order to obtain a general model, a relaxed free energy in small strain theory is defined using variational principles for inelastic materials. This energy includes the dissipation of the substance as so‐called dissipation distance to facilitate a time‐stepped incremental representation. Furthermore, the phase volume fractions are contained in the weighted sum of the individual energies and are expressed here using Young measures. In the centre of the model, transition rates with underlying ordinary differential equations (ODEs) are calculated, which allow access to the phase evolution of the system. The initial results and the behaviour of this theory are explained using numerical simulations created with the programming language Julia.