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Thermo-acoustical waves in thermo-plastic materials

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Summary

The propagation velocities and the variation of the amplitudes of thermo-acoustical waves in thermo-plastic materials are theoretically investigated. The constitutive equations of anisotropic thermo-plastic materials are derived from the concept of imaginary decomposition of the deformation rate tensor into the elastic and plastic contributions and from that of the plastic potential. From generalized Vernotte's heat conduction law the propagation condition of the jumps of the velocity gradients and of the temperature rate is obtained. In isotropic materials and in the case of a normal stress vector on the wave front we have two purely mechanical transverse waves and two thermo-longitudinal coupled waves. Formulae for the velocities and amplitudes are quite similar with those for thermo-elastic materials. The variation of the amplitude is discussed. There are, in general, three effects on the variation, that is, the non-planar, heat conduction and plastic flow effects. The transverse waves are subjected only to the non-planar effect, while the thermo-longitudinal waves may grow or decay according to the above three effects.

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References

  1. T. Tokuoka, Yield conditions and flow rules derived from hypo-elasticity,Arch. Rational Mech. Anal., 42 (1971) 239–252.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. C. Truesdell, Hypo-elasticity,J. Rational Mech. Anal., 4 (1955) 83–133, 1019–1020.

    MATH  MathSciNet  Google Scholar 

  3. T. Tokuoka, Generalized Prandtl-Reuss plastic materials, I. Constitutive equation for finite deformation,Mem. Fac. Engng., Kyoto Univ., 33 (1971) 186–192.

    Google Scholar 

  4. T. Tokuoka, Thermo-hypo-elasticity and derived fracture and yield conditions,Arch. Rational Mech. Anal., 46 (1972) 114–130.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. T. Tokuoka, Constitutive equations of thermo-plastic materials,Trans. Japan Soc. Aero. Space Sci., 16 (1973) 51–59.

    Google Scholar 

  6. P. Vernotte, La véritable équation de la chaleur,Compt. rend. Acad. Sci., 246 (1958) 3154–3155.

    MathSciNet  Google Scholar 

  7. E. B. Popov, Dynamic coupled problem of thermoelasticity for a half-space taking account of the finiteness of the heat propagation velocity,J. Appl. Math. Mech. (PMM), 31 (1967) 349–356.

    MATH  Google Scholar 

  8. J. D. Achenbach, The influence of heat conduction on propagating stress jumps,J. Mech. Phys. Solids, 16 (1968) 273–282.

    Google Scholar 

  9. P. J. Chen, On the growth and decay of one-dimensional temperature rate waves,Arch. Rational Mech. Anal. 35 (1969) 1–15.

    Article  ADS  MATH  Google Scholar 

  10. T. Tokuoka, Thermo-acoustical waves in linear thermo-elastic materials,J. Eng. Math., 7 (1973) 115–122.

    MATH  Google Scholar 

  11. T. Tokuoka, Variation of amplitudes of thermo-acoustical waves of arbitrary form in isotropic linear thermo-elastic materials,J. Eng. Math., 7 (1973) 361–366.

    MATH  Google Scholar 

  12. T. Tokuoka, Generalized Prandtle-Reuss plastic materials, II. Characteristic surfaces and acceleration wave propagation,Mem. Fac. Engng, Kyoto Univ., 33 (1971) 193–200.

    MathSciNet  Google Scholar 

  13. T. Tokuoka, Generalized Prandtl-Reuss plastic materials, III. Growth and decay of acceleration waves and propagating boundary surfaces,Mem. Fac. Engng, Kyoto Univ., 33 (1971) 201–210.

    Google Scholar 

  14. T. Tokuoka, Constitutive equations and wave propagation of anisotropic perfectly plastic materials,Trans. Japan Soc. Aero. Space Sci., 15 (1972) 22–27.

    Google Scholar 

  15. T. Tokuoka, Propagation velocities and amplitudes of thermo-acoustical waves in thermo-plastic materials,Trans. Japan Soc. Aero. Space Sci., (in press).

  16. T. Tokuoka, Growth and decay of thermo-acoustical waves in thermo-plastic materials,Trans. Japan Soc. Aero. Space Sci., 16 (1973) 102–112.

    Google Scholar 

  17. R. von Mises, Mechanik der festen Körper im plastisch deformablen Zustand,Göttingen Nachr. math. phys., K. 1913 (1913) 582–592.

    MATH  Google Scholar 

  18. T. Y. Thomas,Concepts from Tensor Analysis and Differential Geometry, second edition, Academic Press, New York-London (1965).

    Google Scholar 

  19. T. Y. Thomas, Extended compatibility conditions for the study of surfaces of discontinuity in continuum mechannics,J. Math. Mech., 6 (1957) 311–322, 907–908.

    MATH  MathSciNet  Google Scholar 

  20. T. Y. Thomas,Plastic Flow and Fracture in Solids, Academic Press, New York-London (1961).

    Google Scholar 

  21. C. Truesdell and R. Toupin,The Classical Field Theories, Handbuch der Physik III/1, Chap. C., edited by S. Flügge, Springer-Verlag, Berlin-Göttingen-Heidelberg (1960).

    Google Scholar 

  22. B. D. Coleman and M. E. Gurtin, Waves in materials with memory, II. On the growth and decay of one-dimensional acceleration waves,Arch. Rational Mech. Anal., 19 (1965) 239–265.

    ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan

    Tatsuo Tokuoka

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  1. Tatsuo Tokuoka
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Tokuoka, T. Thermo-acoustical waves in thermo-plastic materials. J Eng Math 8, 9–22 (1974). https://doi.org/10.1007/BF02353700

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  • DOI: https://doi.org/10.1007/BF02353700

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