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Acceleration Waves in Nonlinear Thermoelastic Micropolar Media

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Synonyms

Acceleration waves; Micropolar continuum; Thermoelasticity

Definition

By the term “acceleration wave”, we mean an isolated geometric surface that moves relative to the material points, across which the acceleration is discontinuous but the displacement and velocity are continuous. More generally, we call an acceleration wave a propagating surface across which second derivatives of some fields undergo discontinuity jump. In the theory of the nonlinear thermoelastic micropolar continuum (called also Cosserat continuum), acceleration waves relate with some jumps of linear and angular accelerations as well as second derivatives of temperature. Acceleration waves are similar to sound waves in solids; they also relate with the localization of deformations in solids.

Overview

Analytic solutions in the theory of the propagation of nonlinear waves are exceptional, and acceleration waves present one of the exceptions. An acceleration wave (or a wave of weak discontinuity of order 2) is...

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  • DOI: 10.1007/978-94-007-2739-7_922
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References

  1. Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, vol III/3. Springer, Berlin, pp 1–602

    Google Scholar 

  2. Truesdell C (1984) Rational thermodynamics, 2nd edn. Springer, New York

    MATH  Google Scholar 

  3. Kafadar CB, Eringen AC (1971) Micropolar media – I. The classical theory. Int J Eng Sci 9:271–305

    MATH  Google Scholar 

  4. Maugin GA (1974) Acceleration waves in simple and linear viscoelastic micropolar materials. Int J Eng Sci 12:143–157

    MATH  Google Scholar 

  5. Eremeyev VA (2005) Acceleration waves in micropolar elastic media. Doklady Phys 50:204–206

    Google Scholar 

  6. Altenbach H, Eremeyev VA, Lebedev LP, Rendón LA (2010) Acceleration waves and ellipticity in thermoelastic micropolar media. Arch Appl Mech 80:217–227

    MATH  Google Scholar 

  7. Eremeyev VA, Lebedev LP, Altenbach H (2012) Foundations of microplar mechanics. Springer, Heidelberg

    Google Scholar 

  8. Dietsche A, Steinmann P, Willam K (1993) Micropolar elastoplasticity and its role in localization. Int J Plast 9:813–831

    MATH  Google Scholar 

  9. Lebedev LP, Cloud MJ, Eremeyev VA (2010) Tensor analysis with applications in mechanics. World Scientific, Hackensack

    MATH  Google Scholar 

  10. Eringen AC (1999) Microcontinuum field theory. I. Foundations and solids. Springer, New York

    Google Scholar 

  11. Pietraszkiewicz W, Eremeyev VA (2009) On natural strain measures of the non-linear micropolar continuum. Int J Solid Struct 46:774–787

    MATH  Google Scholar 

  12. Nowacki W (1986) Theory of asymmetric elasticity. Pergamon Press, Oxford

    MATH  Google Scholar 

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Correspondence to Victor A. Eremeyev .

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Eremeyev, V.A. (2014). Acceleration Waves in Nonlinear Thermoelastic Micropolar Media. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_922

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