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Bulk Nonlinear Elastic StrainWaves in a Bar with Nanosize Inclusions

  • Igor A. Gula
  • Alexander M. Samsonov (†)
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We obtained the travelling wave solutions to DDE, and, in particular, the strain solitary wave solution, which was shown to be significantly affected by parameters of the inclusions. Moreover we found some critical inaccuracies, committed in papers by others in the derivation of a constitutive equation for the long strain waves in a microstructured medium, revised them, and showed an importance of improvements for correct estimation of wave parameters.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Ioffe Institute of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of Physics, Chemistry and PharmacyUniversity of Southern Denmark (SDU)OdenseDenmark

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