Shell-like Structures pp 571-584

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15) | Cite as

A Variationally Consistent Derivation of Microcontinuum Theories

  • Johannes Meenen
  • Holm Altenbach
  • Victor Eremeyev
  • Konstantin Naumenko
Chapter

Abstract

Micromorphic and micropolar continuum theories can be derived from the classical equations of continuum mechanics by introducing a local averaging technique into a mixed variational principle. This approach delivers the geometrically nonlinear strain measures, the equilibrium equations and the constitutive relations of the microcontinuum theory in a natural, variationally consistent way. It also allows to evaluate the residuum of the locally averaged theory with respect to the underlying classical continuum mechanics, and shows that the microcontinuum can be understood as a special kind of a representative volume element.

Keywords

Microcontinuum Variational principle 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johannes Meenen
    • 1
  • Holm Altenbach
    • 2
  • Victor Eremeyev
    • 2
  • Konstantin Naumenko
    • 2
  1. 1.AachenGermany
  2. 2.Martin-Luther-University Halle-WittenbergHalleGermany

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