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Acceleration Waves in Media with Microstructure

  • Victor A. EremeyevEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 59)

Abstract

Within the unified approach to modelling of media with microstructure we discuss the propagation of acceleration waves. We describe a medium with microstructure as an elastic continuum with strain energy density which depends on deformations and additional internal variable and their first gradients. We use a Nth-order tensor as a kinematical descriptor of the microstructure. By acceleration wave we mean an isolated surface propagating in medium across which second derivatives of some fields undergo discontinuity jump. Here we formulate the conditions of existence of acceleration waves as algebraic inequality expressed using acoustic tensor.

Keywords

Acceleration waves Media with microstructure Acoustic tensor Micropolar medium 

Notes

Acknowledgements

The author acknowledges the Russian Science Foundation (RSCF), for its support within the Project 15–19-10008.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia
  2. 2.The Faculty of Mechanical EngineeringRzeszów University of TechnologyRzeszówPoland

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