Article

Archive for Rational Mechanics and Analysis

, Volume 57, Issue 4, pp 291-323

A continuum theory of elastic material surfaces

  • Morton E. GurtinAffiliated withDepartment of Mathematics, Carnegie-Mellon UniversitySchool of Mathematics & Physics, University of East Anglia
  • , A. Ian MurdochAffiliated withDepartment of Mathematics, Carnegie-Mellon UniversitySchool of Mathematics & Physics, University of East Anglia

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Abstract

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.