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Approaches to Generalized Continua

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Generalized Continua and Dislocation Theory

Part of the book series: CISM Courses and Lectures ((CISM,volume 537))

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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  1. Carlo Sansour

    Present address: The University of Nottingham, UK

Authors and Affiliations

  1. Department of Civil Engineering, INSA Rennes, France

    Carlo Sansour

  2. CERECAM, Department of Civil Engineering, University of Cape Town, South Africa

    Sebastian Skatulla

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  1. University of Nottingham, Nottingham, Great Britain

    Carlo Sansour

  2. CERECAM, Department of Civil Engineering, University of Cape Town, South Africa

    Sebastian Skatulla

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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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