Advertisement

On Edge Interactions and Surface Tension

  • Walter Noll
  • Epifanio G. Virga

Abstract

The idea of a “line distribution of force over the edges of a body” seems to have occurred first to Toupin in 1962 (see p. 403 of [To1]). However, his treatment suffered from the same defect as most treatments of distributions of forces prior to 1960, namely these distributions were only implicit in formulas for resultant forces. The systems of forces giving rise to these resultants were not brought into the open. (See the remark by C. Truesdell in “General References” on p. 156 of [Tr].) The present paper is a first attempt to bring into the open the systems of forces that give rise to distributions of forces over edges.

Keywords

Surface Tension Contact Interaction Regular Surface Internal Side Regular Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [FDSI]
    Noll, W., “Finite-Dimensional Spaces: Algebra, Geometry, and Analysis, Vol. I”, Martinus Nijhoff Publishers, 1987.Google Scholar
  2. [FDSII]
    Noll, W., “Finite-Dimensional Spaces: Algebra, Geometry, and Analysis, Vol. II”, to be published. A preliminary version of Chapt. 3 is available in the form of lecture notes. These notes were the basis of Sect. 3 of [GM].Google Scholar
  3. [F]
    Fraenkel, L. E., “On Regularity of the Boundary in the Theory of Sobolev Spaces”, Proc. London Math. Soc. (3) 39, 385–427 (1979).MathSciNetMATHCrossRefGoogle Scholar
  4. [FV]
    Fosdick, R. L., & E. G. Virga, “A Variational Proof of the Stress Theorem of Cauchy”, Arch. Rational Mech. Anal.105, 95–103 (1989).MathSciNetADSMATHCrossRefGoogle Scholar
  5. [GM]
    Gurtin, M. E., & A. I. Murdoch, “A Continuum Theory of Elastic Material Surfaces”, Arch. Rational Mech. Anal.57, 291–323 (1974).MathSciNetADSGoogle Scholar
  6. [GW]
    Gurtin, M. E., & W. O. Williams, “An Axiomatic Foundation for Continuum Thermodynamics”, Arch. Rational Mech. Anal.26, 83–117 (1967).MathSciNetADSMATHCrossRefGoogle Scholar
  7. [GWZ]
    Gurtin, M. E., W. O. Williams & W. P. Ziemer, “Geometric Measure Theory and the Axioms of Continuum Thermodynamics”, Arch. Rational Mech. Anal.92, 1–22 (1986).MathSciNetADSMATHCrossRefGoogle Scholar
  8. [K]
    Kellogg, O. D., “Foundations of Potential Theory”, Springer, Berlin, 1929.Google Scholar
  9. [N1]
    Noll, W., “The Foundations of Classical Mechanics in the Light of Recent Advances in Continuum Mechanics”, Proceedings of the Berkeley Symposium on the Axiomatic Method, 226–281, Amsterdam, 1959.Google Scholar
  10. [N2]
    Noll, W., “Lectures on the Foundations of Continuum Mechanics and Thermodynamics”, Arch. Rational Mech. Anal.52, 62–92 (1973).MathSciNetADSMATHCrossRefGoogle Scholar
  11. [N3]
    Noll, W., “On Contactors for Surface Interactions”, to appear.Google Scholar
  12. [NV]
    Noll, W., & E. G. Virga, “Fit Regions and Functions of Bounded Variation”, Arch. Rational Mech. Anal.102, 1–21 (1988).MathSciNetADSMATHCrossRefGoogle Scholar
  13. [S]
    Šilhavý, M., “The Existence of the Flux Vector and the Divergence Theorem for General Cauchy Fluxes”, Arch. Rational Mech. Anal.90, 195–212 (1985).MathSciNetADSMATHCrossRefGoogle Scholar
  14. [Tol]
    Toupin, R. A., “Elastic Materials with Couple-stresses”, Arch. Rational Mech. Anal.11, 385–414 (1962).MathSciNetADSMATHCrossRefGoogle Scholar
  15. [To2]
    Toupin, R. A., “Theories of Elasticity with Couple-stress”, Arch. Rational Mech. Anal.17, 85–112 (1964).MathSciNetADSMATHCrossRefGoogle Scholar
  16. [Tr]
    Truesdell, C., “A First Course in Rational Continuum Mechanics”, Vol. I, Academic Press, 1977. Second edition, corrected, revised, and augmented, in press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Walter Noll
    • 1
    • 2
  • Epifanio G. Virga
    • 1
    • 2
  1. 1.Department of MathematicsCarnegie Mellon UniversityPittsburghUSA
  2. 2.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

Personalised recommendations