Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure

A. V. Porubov*, I. E. Berinskii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.

Original languageEnglish
Pages (from-to)94-103
Number of pages10
JournalMathematics and Mechanics of Solids
Volume21
Issue number1
DOIs
StatePublished - Jan 2016
Externally publishedYes

Keywords

  • Nonlinear hexagonal lattice
  • asymptotic solution
  • continuum limit
  • nonlinear differential equation

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