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H. J. Böhm:
"A short tour through continuum micromechanics and multiscale modeling of inhomogeneous materials";
Keynote Lecture: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna (invited); 2019-02-18 - 2019-02-22.

A considerable number of continuum approaches to the homogenization and localization analysis ("upscaling" and "downscaling") of inhomogeneous materials have been developed over the past 150 years. They can be grouped into analytical and bounding schemes as well as numerical approaches based on evaluating the responses of specific inhomogeneous volume elements.
The most important of the pertinent modeling strategies are introduced in a short discussion, special emphasis being put on their respective strengths and weaknesses (as seen from the author´s perspective as engineer). On this basis, the spotlight is directed, on the one hand, on the interplay between analytical and numerical modeling approaches, predictions for some specific inhomogeneous systems being compared. On the other hand, multiscale modeling strategies are discussed that can be obtained by the sequential application of schemes from the above groups and/or by their incorporation into macroscopic models.
The main emphasis is put on matrix-inclusion composites and throughout the presentation specific issues are highlighted that, from the author´s point of view, may merit further detailed study.