Approaches to Generalized Continua

  • Carlo Sansour
  • Sebastian Skatulla
Chapter
Part of the CISM Courses and Lectures book series (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.

Keywords

Strain Measure Strain Gradient Maximum Principal Stress Generalize Continuum Rotation Vector 
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© CISM, Udine 2012

Authors and Affiliations

  • Carlo Sansour
    • 1
  • Sebastian Skatulla
    • 2
  1. 1.Department of Civil EngineeringINSA RennesFrance
  2. 2.CERECAM, Department of Civil EngineeringUniversity of Cape TownSouth Africa

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