Abstract
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.
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Sansour, C., Skatulla, S. (2012). Approaches to Generalized Continua. In: Sansour, C., Skatulla, S. (eds) Generalized Continua and Dislocation Theory. CISM Courses and Lectures, vol 537. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1222-9_2
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