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Spatial interaction in magneto-micropolar continua

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Sommario

Si considera un continuo micropolarc, i cui punti materiali sono dotati di momento magnetico, in presenza di un campo magnetico nell'approssimazione della quasimagnetostatica. Dopo aver dedotto le equazioni di bilancio mediante un opportuno procedimento di media, si esamina la compatibilità tra effetti di interazione spaziale e seconda legge della termodinamica e si mostra che tali effetti possono essere presenti solo nelle equazioni costitutive per lo stress dissipativo (di Cauchy)DT.lo stress dissipativo delle coppieDm e il flusso di calore q. Inoltre, in conseguenza della disuguaglianza di dissipazione ridotta, si osserva che una teoria lineare permetterebbe solo una dipendenza diDT,Dm, q dal gradiente di velocità, dalla velocità angolare, dal gradiente della velocità angolare e dal gradiente di temperatura.

Summary

We consider a micropolar continuum, whose material points are endowed with magnetic moment, in the presence of a magnetic field within the approximation of the quasimagnetostatics. We deduce the balance equations by a suitable averaging technique and then we examine the compatibility of spatial interaction effects with thermodynamics. As a result, we show that such effects are confined to the constitutive equations for the dissipative stressDT, the dissipative couple stressDm and the heat flux q. Moreover, as a consequence of the reduced dissipation inequality, a linear theory would account only for a dependence ofDT,Dm, and q on the velocity gradient, the angular velocity, the gradient of the angular velocity, and on the temperature gradient.

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References

  1. SCOTT G. G., STURNER H. W., WILLIAMSON R. M.,Gas torque anomaly in weak magnetic fields, Phys. Rev.,158, 117–121, 1967.

    Google Scholar 

  2. SMITH G. W., SCOTT G. G.,Measurement of dynamic behavior of the thermomagnetic gas torque effect, Phys. Rev. Lett.,20, 1469–1471, 1968.

    Google Scholar 

  3. LEVI A. C., BEENAKKER J. J. M.,Thermomagnetic torques in dilute gases, Phys. Lett.,25A, 350–352, 1967.

    Google Scholar 

  4. LEVI A. C., McCOURT F. R., BEENAKKER J. J. M.,Burnett coefficients in a magnetic field. II. The linear effects, Physica,42, 363–387, 1969.

    Google Scholar 

  5. CARRASSI M., MORRO A.,The thermodynamic theory of the Maxwellian fluid, Boll. UMI,9, 297–335, 1974.

    Google Scholar 

  6. GURTIN M. E.,Thermodynamics and the possibility of spatial interaction in rigid heat conductors, Arch. Rational Mech. Anal.,18, 335–342, 1965.

    Google Scholar 

  7. GURTIN M. E.,Thermodynamics and the possibility of spatial interaction in elastic materials, Arch. Rational Mech. Anal.,19, 339–352, 1965.

    Google Scholar 

  8. FABRIZIO M.,Una teoria fenomenologica per la termodinamica del campo eletromagnetico, Bull. UMI,4, 708–719, 1971.

    Google Scholar 

  9. MORRO A.,Thermodynamics and spatial interaction in viscoelastic materials, Boll. UMI,10, 355–374, 1974.

    Google Scholar 

  10. COSSERAT E. and F.,Théorie des corps deformables, Paris, Herman (1909).

    Google Scholar 

  11. TRUESDELL C., TOUPIN R. A.,The classical field theories, in «Encyclopedia of Physics», III/1, Springer-Verlag, 1960.

  12. TOUPIN R. A.,Elastic materials with couple-stresses, Arch. Rational Mech. Anal.,11, 385–414, 1962.

    Google Scholar 

  13. MINDLIN R. D., TIERSTEIN H. F.,Effects of couple-stresses in linear elasticity, Arch. Rational Mech. Anal.,11, 415–448, 1962.

    Google Scholar 

  14. ERINGEN A. C.,Foundations of micropolar thermoelasticity, Int. Centre for Mech. Sci., Udine, 1970.

    Google Scholar 

  15. STOJANOVIC R.,Recent developments in the theory of polar continua, Int. Centre for Mech. Sci., Udine, 1970.

    Google Scholar 

  16. KAFADAR C. B., ERINGEN A. C.,Micropolar media. I. The classical theory, Int. J. Engng. Sci.,9, 271–305, 1971.

    Google Scholar 

  17. GRIOLI G.,Elasticità asimmetrica, Ann. Mat. Pura Appl.,50, 389–417, 1960.

    Google Scholar 

  18. GRIOLI G.,Linear micropolar media with constrained rotations, in «Micropolar elasticity», Int. Centre for Mech. Sci., Udine, 1974.

    Google Scholar 

  19. FERRARESE G.,Sulla formulazione intrinseca della dinamica dei continui alla Cosserat, Ann. Mat. Pura Appl., 108, 109–124, 1976.

    Google Scholar 

  20. TIERSTEN H. F.,Coupled magnetomechanical equations for magnetically saturated insulators, J. Math. Phys.,5, 1298–1318, 1964.

    Google Scholar 

  21. TIERSTEN H. F.,Variational principle for saturated magnetelastic insulators, J. Math. Phys.,6, 779–787, 1965.

    Google Scholar 

  22. BROWN W. F.,Magnetoelastic interactions, Springer-Verlag, 1966.

  23. MAUGIN G. A., ERINGEN A. C.,Deformable magnetically saturated media. I. Field equations, J. Math. Phys.,13, 143–155, 1972;II. Constitutive theory, J. Math. Phys.,13, 1334–1347, 1972.

    Google Scholar 

  24. MAUGIN G. A., ERINGEN A. C.,Variational formulation of the relativistic theory of microelectromagnetism, J. Math. Phys.,15, 1494–1499, 1974.

    Google Scholar 

  25. MAUGIN G. A.,Sur la dynamique des milieux déformables magnétisés avec spin magnétique, J. de Mécanique,13, 75–96, 1974.

    Google Scholar 

  26. McCARTHY M. F.,Thermodynamics of deformable magnetic materials with memory, Int. J. Engng Sci.,12, 45–60, 1974.

    Google Scholar 

  27. DIXON R. C., ERINGEN A. C.,A dynamical theory of polar elastic dielectrics. I, Int. J. Engng Sci.,3, 359–377, 1965.

    Google Scholar 

  28. COLEMAN B. D.,Thermodynamics of materials with memory, Arch. Rational Mech. Anal.,17, 1–46, 1964.

    Google Scholar 

  29. MASON M., WEAVER W.,The electromagnetic field, Dover, 1929.

  30. Jackson, J. D.,Classical electrodynamics, Wiley, 1975.

  31. HERRING C., KITTEL C.,On the theory of spin waves in ferromagnetic media, Phys. Rev.,5, 869–880, 1951.

    Google Scholar 

  32. ATKIN R. J., FOX N.,On the frame-dependence of stress and heat flux in polar fluids, Z. angew. Math. Phys.,24, 853–860, 1973.

    Google Scholar 

  33. ATKIN R. J., FOX N.,A multipolar approach to liquid helium II, Acta Mechanica,21, 221–239, 1975.

    Google Scholar 

  34. COLEMAN B. D., NOLL W.,The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal.,13, 167–178, 1963.

    Google Scholar 

  35. TRUESDELL C., NOLL W.,The non linear field theories of mechanics, in «Encyclopedia of Physics», III/3, Springer-Verlag, 1965.

  36. LIANIS G.,The general form of constitutive equations in relativistic physics, Nuovo Cimento,14B, 57–103, 1973.

    Google Scholar 

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Authors and Affiliations

  1. Università di Genova, Istituto di Matematica, via L. B. Alberti 4, 16132, Genova, Italy

    Angelo Morro

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  1. Angelo Morro
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This work was supported by the «Gruppo Nazionale per la Fisica Matematica» of CNR.

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Morro, A. Spatial interaction in magneto-micropolar continua. Meccanica 12, 194–207 (1977). https://doi.org/10.1007/BF02128229

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  • DOI: https://doi.org/10.1007/BF02128229

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