Efficient FE- and FFT-based two-scale methods for micro-heterogeneous media

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Most materials of technological importance are heterogeneous at a certain scale. Typical examples include polycrystalline aggregates, fiber-reinforced composites, high-strength ceramics, and porous media. The overall, macroscopic mechanical behavior of such materials is, to a large extent, determined by physical, topological and statistical details of the underlying - and possibly evolving - microstructure. Thus, the scientific and economic interest in developing continuum mechanical two-scale models that are capable of capturing microstructural features has been growing rapidly and will continue to grow in the long term. At the current stage of research, high fidelity two-scale simulations of complex engineering systems are still barely possible when dealing with inelastic micro-heterogeneous media. This cumulative thesis reports research progress on different fields of modeling multi-phase materials across the scales using fast Fourier transforms (FFT), phase-field approaches, and finite element (FE) methods. The overall goal is the development of efficient FE- and FFT-based two-scale methods for the modeling of bulk microstructural evolution and the elasto-viscoplastic constitutive behavior of polycrystalline media for isothermal deformations at small and finite strains.