For a bonded interface between two membranes, which are considered as material surfaces, it is shown that the continuity of displacements can be represented by the requirement that the tangential strain and the change in curvature and torsion be matched across the interface for the case of infinitesimal deformation. The reduction of these conditions for a two-dimensional bonded interface is also discussed. Finally, it is demonstrated that the continuity of the displacements may not be replaced by the conditions involving only strains.
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References
1.
[1] Dundurs, J.: Cavities vis-a-vis rigid inclusions and some related general results in plane elasticity. ASME J. Appl. Mech., 60, 195-202 (1989).
2.
[2] Dundurs, J.: Boundary conditions at interfaces, in Micromechanics and Inhomogeneity, pp. 109-114, ed., G. J. V Wng, M. Taya, & H. Ab, Springer-Verlag, New York, 1990.
3.
[3] Markenscoff, X. and Wheeler, L.: On conditions at an interface between two materials in plane deformation. J. Elasticity, 45, 33-44 (1996).
4.
[4] Wheeler, L. and Luo, C.: On conditions at an interface between materials in three-dimensional space. MMS, 4, 183-200 (1999).
5.
[5] Markenscoff, X.: A note on strain jump conditions and Cesaro integrals for bonded and slipping inclusions. J. Elasticity, 45, 45-51 (1996).
6.
[6] Naghdi, P M.: Theory of shells and plates, in Handbuch der Physik, vol. VI a/2, pp. 425-640, ed., S. Flugge, Springer-Verlag, New York, 1972.
7.
[7] Steigmann, D. J.: Tension field theory. Proc. Roy. Soc. Lond., A 429, 141-173 (1990).
8.
[8] McCleary, J.: Geometryfiom a Differentiable Viewpoint, Cambridge University Press, Cambridge, UK, 1994.
9.
[9] Sokolnikoff, I. S.: Mathematical Theory of Elasticity, McGraw-Hill, New York, 1956.
