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Nonlocal Approach to Square Lattice Dynamics

  • Alexey V. Porubov
  • Alena E. Osokina
  • Thomas M. Michelitsch
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

The algorithm is developed to model two-dimensional dynamic processes in a nonlocal square lattice on the basis of the shift operators. The governing discrete equations are obtained for local and nonlocal models. Their dispersion analysis reveals important differences in the dispersion curve and in the sign of the group velocity caused by nonlocality. The continuum limit allows to examine possible auxetic behavior of the material described by the nonlocal discrete model.

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Notes

Acknowledgements

The work of AVP and AEO has been supported by the Russian Foundation for Basic Researches, grant No 17-01-00230-a.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alexey V. Porubov
    • 1
    • 2
  • Alena E. Osokina
    • 1
    • 2
  • Thomas M. Michelitsch
    • 3
  1. 1.Institute for Problems in Mechanical Engineering of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Peter the Great St.Petersburg Polytechnic UniversitySt.PetersburgRussia
  3. 3.Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’AlembertSorbonne UniversitéParisFrance

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