Sage Journals: Discover world-class research

Abstract

The following analysis investigates the delamination of an elastic membrane which on one side adheres to a smooth substrate while the other side is attached to a rigid cylindrical shaft. When the shaft is pulled perpendicularly from the substrate, this system is equivalent to the blister test of Malyshev and Salganik (International Journal of Fracture Mechanics, 1, 114 (1965)) and a solution is derived using the principle of minimum potential energy. Delamination can also be caused by rotating the shaft, which may be induced by a shear load and/or moment applied to the free end. For this more complicated system, an approximate solution is obtained from upper and lower bounds on strain energy that are derived from stationary principles with restricted deformation and stress fields, respectively. Beyond their applicability to blister tests, these results are relevant to the emerging study of biologically-inspired adhesives, as membranes constitute a critical attachment structure for a variety of wall-clinging organisms.

Keywords

Non-linear membrane theory stationary principles complementary energy Hencky strain measure

Get full access to this article

View all access options for this article.

References

Malyshev, B.M. and Salganik, R.L. International Journal of Fracture Mechanics , 1, 114 (1965).

Williams, J.G.

International Journal of

Fracture, 87, 265—288 (1997).

Wan, K.-T. and Mai, Y.-W.

International Journal of

Fracture, 74, 181—197 ( 1995).

Wan, K.-T. and Kogut, L. Journal of Micromechanical Microengineering , 15, 778—784 (2005).

Shenoy, V.B. and Freund, L.B. Proceedings of the National Academy of Sciences of the USA, 102, 3213—3218 ( 2005).

Persson, B.N.J. and Gorb, S. Journal of Chemical Physics, 119, 11437—11444 (2003).

Spolenak, R. , Gorb, S. , Gao , H. and Arzt, E. Proceedings of the Royal Society A, 461, 305—319 ( 2004).

Huber, G. , Mantz, H. , Spolenak, R. , Mecke, K. , Jacovs, K. , Gorb, S.N. , Arzt, E. Proceedings of the National Academy of Sciences of the USA, 102, 16293—16296 (2005).

Hansen, W.R. and Autumn, K. Proceedings of the National Academy of Sciences of the USA, 102, 385—389 ( 2004).

10.

Autumn, K. American Scientist, 24, 124—132 (Mar—Apr 2006).

11.

Kahn, J. National Geographic, 209, 98—119 (June 2006).

12.

Autumn, K. , Sitti, M. , Liang , Y.A. , Peattie, A.M. , Hansen, W.R. , Sponberg, S. , Kenny, T.W. , Fearing, R. , Israelachvili, J.N. and Full, R.J. Proceedings of the National Academy of Sciences of the USA, 99, 12252—12256 ( 2002).

13.

Kendall, K. Journal of Physics D: Applied Physics, 4, 1186—1195 (1971).

14.

Haddow, J.B. , Favre, L. and Ogden, R.W.

Journal of Engineering

Mathematics, 37, 65—84 (2000 ).

15.

Koiter, W.T. Trends in Applications of Pure Mathematics to Mechanics, 1, 207—232 (1976).

16.

Liu, S. , Haddow, J.B. and Dost, S. Acta Mechanica , 99, 191—200 (1993).

17.

Steigmann, D.J. International Journal of Non-linear Mechanics , 40, 255—270 (2005).

18.

Ogden, R.W. Non-linear Elastic Deformations, Ellis Horwood , Chichester, 1984.

19.

Valid, R. The Nonlinear Theory of Shells through Variational Principles, Wiley, New York, 1995 .

20.

Gao, D.Y. Duality Principles in Nonconvex Systems, Kluwer, Dordrecht, 2000 .

21.

Anand, L. Journal of Applied Mechanics, 46, 78—82 (1979 ).

22.

Anand, L. Journal of Mechanics and Physics of Solids, 34, 293—304 (1986).

23.

Bertram, A. Elasticity and Plasticity of Large Deformations, Springer , Berlin, 2000.

24.

Anderson, T.L. Fracture Mechanics, 3rd edition, CRC/Taylor and Francis, Boca Raton, FL, 29 (2005).

25.

Troutman, J.L. Variational Calculus and Optimal Control, 2nd edition, Springer, New York, 1996.

26.

Carbone, G. , Mangialardi, L. and Persson, B.N. J. Physical Review B, 70, 125407 (2004).

Analysis of Shaft-Loaded Membrane Delamination Using Stationary Principles

Abstract

Keywords

Get full access to this article

References