Diese Arbeit beschäftigt sich mit der Vorhersage des elastischen Verhaltens von kurzfaserverstärkten Werkstoffen duch Mean-Field-Homogenizierungsmethoden, die experimentell ermittelte und künstlich Mikrostrukturinformationen in diskreter und gemittelter Form berücksichtigen. Die Vorhersagen werden mit Experimenten und mit voxelbasierten Vollfeldlösungen verglichen. Es wird untersucht, ob für solche Vorhersagen der Orientierungstensor zweiter Stufe die Mikrostruktur ausreichend beschreibt. This work is focused on the prediction of elastic behavior of short-fiber reinforced composites by mean-field homogenization methods, which account for experimentally determined and artificially constructed microstructure data in discrete and averaged form. The predictions are compared with experimental measurements and a full-field voxel-based approach. It is investigated, whether the second-order orientation tensor delivers a sufficient microstructure description for such predictions.

This work is dedicated to the numerically efficient simulation of the material response of polycrystalline aggregates. Therefore, crystal plasticity is combined with a new non-linear homogenization scheme, which is based on piecewise constant stress polarizations with respect to a homogeneous reference medium and corresponds to a generalization of the Hashin-Shtrikman scheme. This mean field approach accounts for the one- and two-point statistics of the microstructure.

Silicon nitride is used for challening applications like cutting inserts or forming rolls. The extreme strength and toughness of the material is achieved by an interaction between the microstructure and fracture behaviour on the microlevel. In order to understand these mechanisms, detailed unit cells have been defined and used for the determination of the effective fracture properties. The results have been used for the implementation of an effective continuum damage mechanics model.

This book is a contribution to the further development of gradient plasticity. Several open questions are addressed, where the efficient numerical implementation is particularly focused on. The book inspects an equivalent plastic strain gradient plasticity theory and a grain boundary yield model. Experiments can successfully be reproduced. The hardening model is based on dislocation densities evolving according to partial differential equations taking into account dislocation transport.