Skip to main content
Log in

On the thermomechanics of interstitial working

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Toupin, R. A., Elastic materials with couple-stresses. Arch. Rational Mech. Anal. 11, 385–414 (1962).

    Google Scholar 

  2. Toupin, R. A., Theories of elasticity with couple-stress. Arch. Rational Mech. Anal. 17, 85–112 (1964).

    Google Scholar 

  3. Gurtin, M., Thermodynamics and the possibility of spatial interaction in elastic materials. Arch. Rational Mech. Anal. 19, 339–352 (1965).

    Google Scholar 

  4. Eringen, A. C., A unified theory of thermomechanical materials. Int. J. Engng. Sci. 4, 179–202 (1966).

    Google Scholar 

  5. Fixman, M., Transport coefficients in the gas critical region. J. Chem. Physics. 47, 2808–2818 (1967).

    Google Scholar 

  6. Felderhof, B. U., Dynamics of the diffuse gas-liquid interface near the critical point. Physica 48, 541–560 (1970).

    Google Scholar 

  7. Blinowski, A., On the surface behavior of gradient-sensitive liquids. Arch. Mech. 25, 259–268 (1973).

    Google Scholar 

  8. Blinowski, A., On the order of magnitude of the gradient-of-density dependent part of an elastic potential in liquids. Arch. Mech. 25, 833–849 (1973).

    Google Scholar 

  9. Blinowski, A., Gradient description of capillary phenomena in multicomponent fluids. Arch. Mech. 27, 273–292 (1975).

    Google Scholar 

  10. Blinowski, A., On the phenomenological models of capillary phenomena. Arch. Mech. 31, 423–430 (1979).

    Google Scholar 

  11. Aifantis, E. C., & J. Serrin, The mechanical theory of fluid interfaces and Maxwell's rule. J. Colloid Interface Sci. 96, 517–529 (1983).

    Google Scholar 

  12. Aifantis, E. C., & J. Serrin, Equilibrium solutions in the mechanical theory of fluid microstructures. J. Colloid Interface Sci. 96, 530–547 (1983).

    Google Scholar 

  13. Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal. 81, 301–315 (1983).

    MathSciNet  MATH  Google Scholar 

  14. Slemrod, M., Dynamic phase transitions in a van der Waals fluid. J. Differential Equations 52, 1–23 (1984).

    Google Scholar 

  15. Slemrod, M., An admissibility criterion for fluids exhibiting phase transitions. Nonlinear Partial Differential Equations. Ed.by J. Ball. NATO Advanced Study Institute, Plenum Press: New York, 1982.

    Google Scholar 

  16. Hagan, R., & M. Slemrod, The viscosity-capillarity admissibility criterion for shocks and phase transitions. Arch. Rational Mech. Anal. 83, 333–361 (1983).

    Google Scholar 

  17. Hagan, R., & J. Serrin, Dynamic changes of phase in a van der Waals fluid, To appear in New Perspectives in Thermodynamic, Springer-Verlag, 1985.

  18. Serrin, J., The form of interfacial surfaces in Korteweg's theory of phase equilibria. Q. Appl. Math., 41, 351–364 (1983).

    Google Scholar 

  19. Cheverton, K. J., & M. F. Beatty, On the mathematical theory of the mechanical behavior of some non-simple materials. Arch. Rational Mech. Anal. 60, 1–16 (1975).

    Google Scholar 

  20. Beatty, M. F., & K. J. Cheverton, The basic equations for a grade 2 material viewed as an oriented continuum. Arch. Mech. 28, 205–213 (1976).

    Google Scholar 

  21. Murdoch, A. I., Symmetry considerations for materials of second grade. J. Elasticity 9, 43–50 (1979).

    Google Scholar 

  22. Ericksen, J. L., Conservation laws for liquid crystals. Trans. Soc. Rheology 5, 23–34 (1961).

    Google Scholar 

  23. Truesdell, C., & W. Noll, The Non-Linear Field Theories of Mechanics. Flügge's Handbuch der Physik, III/3. Berlin-Heidelberg-New York: Springer, 1965.

    Google Scholar 

  24. Müller, I., On the entropy inequality. Arch. Rational Mech. Anal. 26, 118–141 (1967).

    Google Scholar 

  25. Eringen, A. C., Nonlocal polar elastic continua. Int. J. Engng. Sci. 10, 1–16 (1972).

    Google Scholar 

  26. Eringen, A. C., & D. G. B. Edelen, On nonlocal elasticity. Int. J. Engng. Sci. 10, 233–248 (1972).

    Google Scholar 

  27. Eringen, A. C., On nonlocal fluid mechanics. Int. J. Engng. Sci. 10, 561–575 (1972).

    Google Scholar 

  28. Aifantis, E. C., A proposal for continuum with microstructure. Mech. Res. Comm. 5, 139–145 (1978).

    Google Scholar 

  29. Coleman, B. D., & V. J. Mizel, Existence of caloric equations of state in thermodynamics. J. Chem. Physics 40, 1116–1125 (1964).

    Google Scholar 

  30. Noll, W., Representations of certain isotropic tensor functions. Arch. Math. 21, 87–90 (1970).

    Google Scholar 

  31. Dunn, J. E., Interstitial working and a nonclassical continuum thermodynamics. To appear, New Perspectives in Thermodynamics, Springer-Verlag, 1985.

  32. Coleman, B. D., & V. J. Mizel, Thermodynamics and departures from Fourier's law of heat conduction. Arch. Rational Mech. Anal. 13, 245–261 (1963).

    Google Scholar 

  33. Green, A. E., & R. S. Rivlin, Simple force and stress multipoles. Arch. Rational Mech. Anal. 16, 325–353 (1964).

    Google Scholar 

  34. Green, A. E., & R. S. Rivlin, Multipolar continuum mechanics. Arch. Rational Mech. Anal. 17, 113–147 (1964).

    Google Scholar 

  35. Gurtin, M. E., & L. S. Vargas, On the classical theoty of reacting fluid mixtures. Arch. Rational Mech. Anal. 43, 179–197 (1971).

    Google Scholar 

  36. Olver, P. J., Conservation laws and null divergences. Math. Proc. Camb. Phil. Soc. 94, 529–540 (1983).

    Google Scholar 

  37. Olver, P. J., Conservation laws and null divergences. II Nonnegative divergences. Math. Proc. Camb. Phil. Soc. To appear.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to J. L. Ericksen on his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dunn, J.E., Serrin, J. On the thermomechanics of interstitial working. Arch. Rational Mech. Anal. 88, 95–133 (1985). https://doi.org/10.1007/BF00250907

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00250907

Keywords

Navigation