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Inertial and self interactions in structured continua: Liquid crystals and magnetostrictive solids

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Abstract

Evolution equations for liquid crystals and for magnetostrictive solids are discussed within the framework of a theory of continua with microstructure that allows for mechanical self-interactions and non-standard inertial terms.

Sommario

Si discutono equazioni di evoluzione per cristalli liquidi e per solidi magnetostrittivi nell'ambito di una teoria dei continui con microstruttura che contempla la possibilità sia di autointerazioni meccaniche che di termini inerziali non standard.

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References

  1. Brown, W.F., ‘Electric and magnetic forces: a direct calculation’,Am. J. Phys.,19 (1951), 290–304 and 333–350.

    Google Scholar 

  2. Brown, W.F.,Micromagnetics, John Wiley & Sons (Interscience), 1963.

  3. Brown, W.F.,Magnetoelastic Interactions, Springer-Verlag, 1966.

  4. Chandrasekhar, S.,Liquid Crystals, 2nd ed., Cambridge University Press, 1992.

  5. DeGennes, P.G. and Prost, J.P.,The Physics of Liquid Crystals, 2nd ed., Clarendon Press, 1993.

  6. DeSimone, A. and Podio Guidugli, P., ‘On the continuum theory of deformable ferromagnetic solids’, to appear inArch. Rat. Mech. Anal. (1995).

  7. Ericksen, J.L., ‘Anisotropic fluids’,Arch. Rat. Mech. Anal.,4 (1960), 231–237.

    Google Scholar 

  8. Ericksen, J.L., ‘Conservation laws for liquid crystals’,Trans. Soc. Rheol.,5 (1961), 23–34.

    Google Scholar 

  9. Feynman, R.,The Feynman Lectures on Physics, Addison-Wesley, 1964, Vol. 2, Chapter 34.

  10. Gurtin, M.E. and Podio Guidugli, P., ‘On the formulation of balance laws for structured continua’,Z.A.M.P.,43 (1992), 181–190.

    Google Scholar 

  11. Gurtin, M.E. and Williams, W.O., ‘On the first law of thermodynamics’,Arch. Rat. Mech. Anal.,42 (1971), 77–92.

    Google Scholar 

  12. Leslie, F.M., ‘Some constitutive equations for liquid crystals’,Arch. Rat. Mech. Anal.,28 (1968), 265–283.

    Google Scholar 

  13. Maugin, G.A.,Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam, 1988.

    Google Scholar 

  14. Marrucci, G. and Greco, F., ‘Flow behavior of liquid crystalline polymers’, in Prigogine, I. and Rice, S.A. (Eds),Advances in Chemical Physics, Volume LXXXVI, John Wiley & Sons, 1993, pp. 331–404.

  15. Podio Guidugli, P., ‘Inertia and invariance’,Annali Mat. Pura Appl., in press, (1994).

  16. Serrin, J., ‘The equations of continuum mechanics as a consequence of invariance and thermodynamical principles’,Lecture at the Conference on Nonlinear Analysis and Partial Differential Equations, Rutgers University, May 1990.

  17. Serrin, J., ‘The equations of continuum mechanics as a consequence of group invariance’,Lecture at the Conference on Advances in Modern Continuum Dynamics, Isola d'Elba, June 1991.

  18. Tiersten, H.F., ‘Coupled magnetomechanical equations for magnetically saturated insulators’,J.Math. Phys.,5 (1964), 1298–1318.

    Google Scholar 

  19. Tiersten, H.F.,A Development of the Equations of Electromagnetism in Material Continua, Springer-Verlag, 1990.

  20. Williams, W.O., Review ofContinua with Microstructure, by G. Capriz, Springer-Verlag, 1989.SIAM Review 33, (1991), 161–163.

    Google Scholar 

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Desimone, A., Guidugli, P.P. Inertial and self interactions in structured continua: Liquid crystals and magnetostrictive solids. Meccanica 30, 629–640 (1995). https://doi.org/10.1007/BF01557090

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  • DOI: https://doi.org/10.1007/BF01557090

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