Skip to main content
Log in

A continuum theory of elastic material surfaces

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


A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others


  • 1928 Lennard-Jones, J. E., & B. M. Dent, Change in lattice spacing at crystal boundary. Proc. Roy. Soc. A 121, 247–259.

    Google Scholar 

  • 1930 Lennard-Jones, J. E., Note on the dependence of crystal spacing on crystal size. Zeits. f. Kristallog. 75, 215–216.

    Google Scholar 

  • 1932 Orowan, E., Bemerkung zu den Arbeiten von F.Zwicky über die Struktur der Realkristalle. Zeits. f. Physik. 79, 573–582.

    Google Scholar 

  • 1941 Adam, N. K., The Physics and Chemistry of Surfaces, 3rd edition. London: Oxford University Press.

    Google Scholar 

  • 1950 Shuttleworth, R., The surface tension of solids. Proc. Phys. Soc. A 63, 444–457.

    Google Scholar 

  • 1953 Herring, C,The use of classical macroscopic concepts in surface energy problems, in Structure and Properties of Solid Surfaces (ed. R. Gomer & C.S. Smith). University of Chicago Press.

  • 1958 Halmos, P.R., Finite-dimensional Vector Spaces. Princeton-Toronto-London-New York: Van Nostrand.

    Google Scholar 

  • 1959 Landau, L.D., & E.M. Lifshitz, Fluid Mechanics. London-Paris-Frankfurt: Pergamon.

    Google Scholar 

  • 1960 Scriven, L.E., Dynamics of a fluid interface. Chem. Eng. Sc. 12, 98–108.

    Article  MATH  Google Scholar 

  • 1960 Truesdell, C., & R. Toupin, The Classical Field Theories. In Handbuch der Physik, Vol. III/1 (ed. S. Flügge). Berlin-Göttingen-Heidelberg: Springer.

    Google Scholar 

  • 1964 Nadeau, G., Introduction to Elasticity. New York-Chicago-San Francisco-Toronto-London: Holt, Rinehart & Wilson.

    Google Scholar 

  • 1965 Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik, Vol. III/3 (ed. S. Flügge). Berlin-Heidelberg-New York: Springer.

    Google Scholar 

  • 1966 Truesdell, C., The Elements of Continuum Mechanics. New York: Springer.

    Google Scholar 

  • 1967 Adamson, A.W., Physical Chemistry of Surfaces. New York-London: Interscience.

    Google Scholar 

  • 1968 Fisher, G.M.C., & M.J. Leitman, On continuum thermodynamics with interfaces. Arch. Rational Mech. Anal. 30, 225–262.

    Google Scholar 

  • 1968 Goodier, J.N., Mathematical theory of equilibrium cracks. In Fracture an Advanced Treatise. Vol. II (ed. H. Liebowitz). New York-London: Academic Press.

    Google Scholar 

  • 1970 Orowan, E., Surface energy and surface tension in solids and fluids. Proc. Roy. Soc. A 316, 473–491.

    Google Scholar 

  • 1972 Gurtin, M.E., The Linear Theory of Elasticity. In Handbuch der Physik, Vol. VIa/2 (ed. C. Truesdell). Berlin-Heidelberg-New York: Springer.

    Google Scholar 

  • 1972 Naghdi, P.M., The Theory of Shells and Plates. In Handbuch der Physik, Vol. VIa/2 (ed. C. Truesdell). Berlin-Heidelberg-New York: Springer.

    Google Scholar 

  • 1972 Williams, W.O., Axioms for work and energy in general continua. II. Surfaces of discontinuity. Arch. Rational Mech. Anal. 49, 225–240.

    Google Scholar 

  • 1973 Noll. W., Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal. 52, 62–92.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Gurtin, M.E., Ian Murdoch, A. A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal. 57, 291–323 (1975).

Download citation

  • Received:

  • Issue Date:

  • DOI: