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Dynamics of the Euler Buckling Instability

Published online by Cambridge University Press:  21 March 2011

Leonardo Golubovic
Leonardo Golubovic*
Affiliation:
Department of Physics, West Virginia University, Morgantown, WV 26506
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Abstract

We review recent systematic investigations of the dynamics of the classical Euler buckling of compressed solid membranes and thin sheets. We relate the membrane buckling dynamics to phase ordering phenomena. Evolving membranes develop wavelike patterns whose wavelength grows, via coarsening, as a power of time. We find that evolving membranes are similar to interfaces of thin films in molecular-beam epitaxy growth with slope selection: They are characterized by the presence of mounds whose typical size grows as a power of time. The morphologies of the evolving membranes are characterized by the presence of a network of growing ridges where the elastic energy is mostly concentrated. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our findings show that the membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 672: Symposium O – Mechanisms of Surface and Microstructure Evolution in Deposited Films and Film Structures , 2001 , O5.5
Copyright
Copyright © Materials Research Society 2001

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References

REFERENCES

1. Kantor, Y., Kardar, M., and Nelson, D. R., Phys. Rev. Lett. 57, 791 (1986); Phys. Rev. A 35, 3056 (1987).Google Scholar
2. Abraham, F. F., Rudge, W. E. and Plischke, M., Phys. Rev. Lett. 62, 1757 (1989).Google Scholar
3. Grest, G. S. and Murat, M., J. Phys. (France) 51, 1415 (1990).Google Scholar
4. Grest, G. S. and Petsche, I. B., Phys. Rev. E 50, 1737 (1994).Google Scholar
5. Kroll, D.M. and Gompper, G., J. Phys. (France) I 3, 1131 (1993).Google Scholar
6. Hwa, T., Kokufuta, E. and Tanaka, T., Phys. Rev. A 44, 2235 (1991).Google Scholar
7. Spector, M.S., Naranjo, E., Chiruvolu, S. and Zasadzinski, J. A., Phys. Rev. Lett. 73, 2867–2870 (1994).Google Scholar
8. Aronowitz, J.A. and Lubensky, T.C., Euro-phys. Lett. 4, 395 (1987).Google Scholar
9. Nelson, D.R. and Peliti, L., J. Phys. (France) 48, 1085 (1987); J. A. Aronowitz, L. Golubovic and T. C. Lubensky, J. Phys. (France) 50, 609 (1989)Google Scholar
10. Kardar, M. and Nelson, D. R., Phys. Rev. Lett. 58, 1289 (1987); F. David and K.J. Wiese, Phys. Rev. Lett. 76, 4564 (1996).Google Scholar
11. Moldovan, D. and Golubovic, L., Phys. Rev. Lett. 82, 2884 (1999), and Phys. Rev. E 60, 4377 (1999).Google Scholar
12. Golubovic, L., Moldovan, D., and Peredera, A., Phys. Rev. Lett. 81, 3387 (1998), and Phys. Rev. E 61, 1703 (2000).Google Scholar
13. Landau, L.D. and Lifshitz, E.M., Theory of Elasticity (Pergamon, 1986); A. E. Love, A Treatise on the Mathematical Theory of Elasticity, (Dover 1994), Chapter 2.Google Scholar
14. Stutenkemper, P. and Brasche, R., in Proceedings of the Seventh International Conference on Experimental Safety Vehicles, Paris, 1979 (U.S. Department of Transportation, Washington, D.C., 1980).Google Scholar
15. Sackmann, E., Eggl, P., Fahn, C., Ringsdorf, H. and Schollmeier, M., J. Phys. Chem. 89,1198 (1985).Google Scholar
16. Chianelli, R. R., Prestige, E. B., Pecoraro, T. A. and DeNeufville, J.P., Science 203,1105 (1979).Google Scholar
17. Schmidt, C.F.et al., Science 259, 952 (1993).Google Scholar
18. Bordieu, L.et al., Phys. Rev. Lett. 72, 1502 (1994); A. Saint-Jalmes and F. Gallet, European Physical Journal B, vol 2, no. 4, 498(1998).Google Scholar
19.For buckling induced by internal strains, see, for example, the special issue Heteroepitaxy and Strain, Bull. Int. MRS 21, No. 4 (1996). For thermally induced buckling, see Huntz, A. M., Materials Science and Engineering A201, 211 (1995).Google Scholar
20. Binder, K., Rep. Prog. Phys. 50, 783 (1987).Google Scholar
21. Furukawa, H., Adv. in Phys. 34, 703 (1985).Google Scholar
22. Bray, A. J., Adv. in Phys. 43, 357 (1994).Google Scholar
23. Ernst, H.-J.et al., Phys. Rev. Lett. 72, 112 (1994); M. D. Johnson, et al., Phys. Rev. Lett. 72, 116 (1994); J. Amar and F. Family, Phys. Rev. B 54, 14742 (1996).Google Scholar
24. Golubovic, L. and Karunasiri, R.P.U., Phys. Rev. Lett. 66, 3156 (1991).Google Scholar
25. Golubovic, L., Phys. Rev. Lett. 87, 90 (1997).Google Scholar
26. Lobkovsky, A. E.et al., Science 270, 1482 (1995); A. E. Lobkovsky, Phys. Rev. E 53, 3750 (1996).Google Scholar
27. Kramer, E. M. and Witten, T., Phys Rev Lett. 78, 1303 (1997).Google Scholar
28.For Zimm effects, see, e.g., Frey, E. and Nelson, D.R., J. Phys. I (France) 1, 1715 (1991), and references therein.Google Scholar
29. Moldovan, D. and Golubovic, L., Phys. Rev. E 61, 6190 (2000).Google Scholar
30.See Ref. 12, Chapter 5.Google Scholar
31. Drasdo, D., Phys. Rev. Lett. 84, 4244 (2000).Google Scholar
32. Huck, W.T.S., Bowden, N., Onck, P., Pardoen, T., Hutchison, J.W., and Whitesides, G.M., Langmuir 16, 3497 (2000).Google Scholar