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Morphological instability and contraction of a rectangular plate under stress

Published online by Cambridge University Press:  21 December 2004

J. Colin*
Affiliation:
Laboratoire de Métallurgie Physique, SP2MI, Bd 2, Teleport 2, BP 30179, 86960 Poitiers-Futuroscope Cedex, France
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Abstract

The contraction of a stressed rectangular plate-like sample has been investigated considering the mechanical stability of its two lateral free surfaces with respect to localized perturbation. The energy variation of the plate has been calculated to determine the condition of development of symmetric and non-symmetric wavelet fluctuations of the two lateral free surfaces when a constant and homogeneous stress is applied to the plate. The contraction has been then studied when a source of non-homogeneous strain is embedded into the plate.

Keywords

Type
Research Article
Copyright
© EDP Sciences, 2005

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References

C. Herring, Structure and Properties of Solid Surfaces (Gomer, Smith Eds., Univ. Chicago Press, 1953)
Mullins, W.W., J. Appl. Phys. 28, 333 (1957) CrossRef
Freund, L.B., Int. J. Solids Struct. 32, 911 (1995) CrossRef
Srolovitz, D.J., Acta Metall. 37, 621 (1989) CrossRef
Grinfeld, M.A., Sov. Phys. Dokl. 31, 831 (1986)
Asaro, R.J., Tiller, W.A., Metall. Trans. 3, 1789 (1972) CrossRef
Junqua, N., Grilhé, J., Philos. Mag. A 71, 1125 (1994) CrossRef
Kirill, D.J., Davis, S.H., Mikisis, M.J., Voorhees, P.W., Proc. R. Soc. London A 455, 3825 (1999) CrossRef
Kirill, D.J., Davis, S.H., Mikisis, M.J., Voorhees, P.W., Interfaces Free Boundaries 4, 371 (2002) CrossRef
Colin, J., Thilly, L., Lecouturier, F., Peyrade, J.P., Askenazy, S., Grilhé, J., Acta Mater. 47, 2761 (1999) CrossRef
Grinfeld, M.A., Acta Mater. 46, 631 (1998) CrossRef
Spencer, B.J., Voorhees, P.W., Davis, S.H., Phys. Rev. Lett. 67, 3696 (1991) CrossRef
P. Nozières, Solids Far From Equilibrium, edited by C. Godrech (Cambridge University Press, Cambridge 1992), pp. 1–54
Spencer, B.J., Meiron, D.I., Acta Mater 42, 3629 (1994) CrossRef
Kassner, K., Misbah, C., Europhys. Lett. 28, 245 (1994) CrossRef
Kassner, K., Misbah, C., Europhys. Lett. 46, 217 (1999) CrossRef
Muller, J., Grant, M., Phys. Rev. Lett. 82, 1736 (1999) CrossRef
Jonsdottir, F., Modell. Simul. Mater. Sci. Eng. 3, 503 (1995) CrossRef
Gao, H.J., J. Mech. Phys. Solids 42, 741 (1994) CrossRef
Chiu, C.H., Gao, H.J., Int. J. Solids Struct. 30, 2983 (1993)
Colin, J., Grilhé, J., Junqua, N., Acta Mater. 46, 1249 (1998) CrossRef
Colin, J., Grilhé, J., Philos. Mag. A 82, 2609 (2002) CrossRef
S. Timoshenko, J.N. Goodier, Theory of elasticity (Mc Graw-Hill, New York, 1951)
Mindlin, R.D., Physics 7, 195 (1936) CrossRef
Eshelby, J.D., Proc. R. Soc. London A 241, 376 (1957) CrossRef
T. Mura, Micromechanics of defects in solids (Martinus Nijhoff Publishers, Dordrecht, 1987), pp. 1–74