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Archive of Applied Mechanics

, Volume 80, Issue 3, pp 217–227 | Cite as

Acceleration waves and ellipticity in thermoelastic micropolar media

  • Holm Altenbach
  • Victor A. Eremeyev
  • Leonid P. Lebedev
  • Leonardo A. Rendón
Original

Abstract

Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented.

Keywords

Acceleration waves Micropolar continuum Cosserat continuum Nonlinear thermoelasticity 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Holm Altenbach
    • 1
  • Victor A. Eremeyev
    • 2
  • Leonid P. Lebedev
    • 3
  • Leonardo A. Rendón
    • 3
  1. 1.Lehrstuhl für Technische Mechanik, Zentrum für IngenieurwissenschaftenMartin-Luther-Universität Halle-WittenbergHalle (Saale)Germany
  2. 2.South Scientific Center of RASci and South Federal UniversityRostov on DonRussia
  3. 3.Universidad Nacional de ColombiaBogotáColombia

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