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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. [ABSTRACT FROM AUTHOR]

The prevalence of osteoporosis is about one in three for women and one in five for men over the age of fifty, making it the most common bone disease worldwide. The disease is characterized by a reduction of the amount of volume percent of cortical bone, weakening the bone and increasing the likelihood of fractures. Modeling and numerical simulations can be used to better understand effects observed in measurements and thus the workings of human bones. Furthermore, they can be used to support the development of new diagnostic tools such as sonography. For this purpose, in previous contributions we developed a two‐scale bone model that considers mechanical, electric and magnetic effects. To connect the scales, we resorted to the finite element square method FE2${\text{FE}}^{2}$. For diagnostics, the main quantity of interest is the resulting magnetic field strength, which can be used to draw conclusions about the bone health. In this contribution, we investigate the influence of the used microstructure model in detail. We created different representative volume elements (RVEs), which are for example, randomly orientated, anisotropic, or differ in shape or mesh resolution. In addition, we consider the use of different shape functions in the finite element calculation. We compare our findings with previous results, which were obtained using only regular RVEs. We investigate the extent, to which the microscale results and the overall macroscale simulation results are affected by the choice of the RVE. [ABSTRACT FROM AUTHOR]