Archive for Rational Mechanics and Analysis

, Volume 57, Issue 4, pp 291–323 | Cite as

A continuum theory of elastic material surfaces

  • Morton E. Gurtin
  • A. Ian Murdoch


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.


Neural Network Residual Stress Complex System Mechanical Behavior Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Morton E. Gurtin
    • 1
    • 2
  • A. Ian Murdoch
    • 1
    • 2
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburgh
  2. 2.School of Mathematics & PhysicsUniversity of East AngliaNorwichEngland

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