Generalized Continuum Mechanics: Various Paths

Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 196)

Abstract

This chapter focuses on a field of continuum mechanics that belongs almost entirely to the twentieth century, so called generalized continuum mechanics. First, a special effort is produced to define this term which essentially means going beyond the traditional view of Cauchy—with the notion of stress introduced by this early nineteenth-century scientist. Three possible paths to such a generalization are discussed with the related mention of main scientific contributors: involving an additional microstructure at each material point in addition to the traditional translational degree of freedom (e.g., micromorphic media, Cosserat continua, in modern times works by Eringen and others), or a better analytic description of the displacement field at each material point by introducing higher order gradients of this displacement in the energy density (e.g., in a theory mostly expanded by Mindlin), or else calling for a truly nonlocal theory that leads to considering spatial functionals for the constitutive equations—this follows contributors such as Kröner, Rogula, Kunin, and Eringen. A more drastic “generalization” started in the mid 1950s involves a loss of the Euclidean nature of the material manifold, as may apply in a densely defective crystal. In each case, the pioneers are mentioned and the most recent formulations are briefly sketched out.

Keywords

Material Point Couple Stress Internal Degree Gradient Theory Nonlocal Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’Alembert UniversitéParis Cedex 05France

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