2012 | OriginalPaper | Buchkapitel
Approaches to Generalized Continua
verfasst von : Carlo Sansour, Sebastian Skatulla
Erschienen in: Generalized Continua and Dislocation Theory
Verlag: Springer Vienna
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Decades ago, it has been recognized that for some materials the kinematics on meso- and micro-structural scale needs to be considered, if the material’s resistance to deformation exhibits a finite radius of interaction on atomic or molecule level, e.g. (1963); (1964) outlined that this is the case if the deformation wave length approaches micro-structural length scale. Differently said, if the external loading corresponds material entities smaller than the
representative volume element
(RVE), then the statistical average of the macro-scopical material behaviour does not hold anymore. In this sense the fluctuation of deformation on micro-structural level as well as relative motion of micro-structural constituens, such as granule, crystalline or other heterogeneous aggregates, influence the material response on macro-structural level. Consequently, field equations based on the assumption of micro-scopically homogeneous material have to be supplemented and enriched to also include non-local and higher-order contributions.