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Classification of Gradient Adhesion Theories Across Length Scale

  • Sergey LurieEmail author
  • Petr Belov
  • Holm Altenbach
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 42)

Abstract

The sequence of continuum theories of adhesion is discussed. We give a brief analysis of the existing theories of adhesion and present a continuum theory of adhesion as a natural generalization of appropriate options for the theory of elasticity and gradient theories of elasticity. We offer a sequence of variational formulations of theories of adhesion and constitutive equations. In addition, the analysis of the structures of the tensors of adhesive elastic modules is presented. As a result, we propose a classification of theories of adhesion and gradient theories of elasticity in terms accounting for scale effects. The classification is based on the qualitative analysis of scale effects of different orders depending on the physical properties of the continuum.

Notes

Acknowledgments

This work was supported by the Russian Foundation for Basic Research project No. 15-01-03649-a.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Problem of Mechanics of RAS and Institute of Applied Mechanics of RASMoscowRussia
  2. 2.Institute of Research, Development and Technology TransferMoscowRussia
  3. 3.Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für MaschinenbauOtto-von-Guericke-Universtät MagdeburgMagdeburgGermany

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