 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 47, Issue 6 / 2012 | Next article >> |
| N.F. Morozov and P.E. Tovstik, "Buckling Modes of a Compressed Plate on an Elastic Substrate," Mech. Solids. 47 (6), 622-627 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
6 |
Pages |
622-627 |
| DOI |
10.3103/S0025654412060027 |
| Title |
Buckling Modes of a Compressed Plate on an Elastic Substrate |
| Author(s) |
N.F. Morozov (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, morozov@nm1016.spb.edu)
P.E. Tovstik (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru) |
| Abstract |
The buckling modes of a homogeneously compressed elastic plate on a soft elastic substrate are studied. The critical compression is uniquely determined by the bifurcation equation, but this compression is associated with a wide set of buckling modes. It was proved that any solution of the Helmholtz equation satisfies the bifurcation equation. At the same time, in microelectronics, it is required to know which buckling mode is realized. Experimental and theoretical investigations show that the chessboard-like buckling mode should be expected. In what follows, this problem is discussed theoretically. The expected buckling mode can be found by analyzing the energy of the initial postcritical deformation, and the desired mode is determined from the condition of its minimum. The analytic expression of this energy is obtained. Its minimization results in the chessboard-like buckling mode. |
| Keywords |
plate, stability, elastic substrate, chessboard-like buckling mode, supercritical deformation |
| References |
| 1. | N. F. Morozov and P. E. Tovstik,
"On Modes of Buckling for a Plate on an Elastic Foundation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 519-528 (2010)
[Mech. Solids (Engl. Transl.)
45 (4), 519-528 (2010)]. |
| 2. | P. E. Tovstik,
"Bulk and Surface Loss of Stability of Transversally Isotropic Material in Compression,"
Vestnik S.-Peterburg. Univ. Ser. 1,
No. 1, 127-133 (2010). |
| 3. | N. F. Morozov and P. E. Tovstik,
"Bulk and Surface Stability Loss of Materials,"
in Multiscaling of Synthetic and Natural Systems with Self-Adaptive Capacity
(Taiwan, 2010),
pp. 27-30. |
| 4. | R. V. Goldstein, V. A. Gorodtsov, and P. S. Shushpannikov,
"Simulation of Stress-Strain State in SiGe Island Heterostructures,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 7-21 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 312-323 (2010)]. |
| 5. | N. Bowden, S. Brittain, A. G. Evans, et al.,
"Spontaneous Formation of Ordered Structures in Thin Films of Metals
Supported on Elastomeric Polymer,"
Lett. Nature
393, 146-149 (1988). |
| 6. | N. F. Morozov, M. V. Paukshto, and P. E. Tovstik,
"Stability of a Surface Layer under a Thermal Loading,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 130-139 (1998)
[Mech. Solids (Engl. Transl.)
33 (1), 106-113 (1998)]. |
| 7. | B. Audoly and A. Boudaoud,
"Buckling of a Thin Film Bound to a Compliant Substrate,"
J. Mech. Phys. Solids
56 (7), 2401-2421, 2444-2458 (2008). |
| 8. | L. E. Panin and V. E. Panin,
"`Chessboard' Effect and Mass Transfer in Interfacial Media of Organic and Inorganic Nature,"
Fizich. Mezomekh.
10 (6), 5-20 (2007)
[Phys. Mesomech. (Engl. Transl.)
11 (1-2), 5-18 (2008)]. |
| 9. | N. F. Morozov and P. E. Tovstik,
"Buckling Forms of a Compressed Plate on an Elastic Foundation,"
Dokl. Ross. Akad. Nauk
446 (1), 37-41 (2012)
[Dokl. Phys. (Engl. Transl.)
57 (9), 335-339 (2012)]. |
| 10. | X. Chen and J. W. Hutchinson,
"Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates,"
Trans. ASME. J. Appl. Mech.
71, 597-603 (2004). |
|
| Received |
18 July 2012 |
| Link to Fulltext |
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