The mechanical system considered is a bilayer cantilever plate. The substrate and the film are linear elastic. The film is subjected to isotropic uniform prestresses due for instance to volume variation associated with cooling, heating, or drying. This loading yields deflection of the plate. We recall Stoney’s analytical formula linking the total mechanical stresses to this deflection. We also derive a relationship between the prestresses and the deflection. We relax Stoney’s assumption of very thin films. The analytical formulas are derived by assuming that the stress and curvature states are uniform and biaxial. To quantify the validity of these assumptions, finite element calculations of the three-dimensional elasticity problem are performed for a wide range of plate geometries, Young’s and Poisson’s moduli. One purpose is to help any user of the formulas to estimate their accuracy. In particular, we show that for very thin films, both formulas written either on the total mechanical stresses or on the prestresses, are equivalent and accurate. The error associated with the misfit between our theorical study and numerical results are also presented. For thicker films, the observed deflection is satisfactorily reproduced by the expression involving the prestresses and not the total mechanical stresses.
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e-mail: mourad.chekchaki@etu.upmc.fr
e-mail: veronique.lazarus@upmc.fr
e-mail: joel.frelat@upmc.fr
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January 2011
Research Papers
Analytical and 3D Finite Element Study of the Deflection of an Elastic Cantilever Bilayer Plate
M. Chekchaki,
e-mail: mourad.chekchaki@etu.upmc.fr
M. Chekchaki
CNRS
, UPMC Univ Paris 6, Univ Paris-Sud, UMR 7608, Lab FAST, Bât 502, Campus Univ, F-91405 Orsay, France
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V. Lazarus,
e-mail: veronique.lazarus@upmc.fr
V. Lazarus
CNRS
, UPMC Univ Paris 6, Univ Paris-Sud, UMR 7608, Lab FAST, Bât 502, Campus Univ, F-91405 Orsay, France
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J. Frelat
e-mail: joel.frelat@upmc.fr
J. Frelat
CNRS
, UPMC Univ Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, F-75005, Paris, France
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M. Chekchaki
CNRS
, UPMC Univ Paris 6, Univ Paris-Sud, UMR 7608, Lab FAST, Bât 502, Campus Univ, F-91405 Orsay, Francee-mail: mourad.chekchaki@etu.upmc.fr
V. Lazarus
CNRS
, UPMC Univ Paris 6, Univ Paris-Sud, UMR 7608, Lab FAST, Bât 502, Campus Univ, F-91405 Orsay, Francee-mail: veronique.lazarus@upmc.fr
J. Frelat
CNRS
, UPMC Univ Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, F-75005, Paris, Francee-mail: joel.frelat@upmc.fr
J. Appl. Mech. Jan 2011, 78(1): 011008 (7 pages)
Published Online: October 13, 2010
Article history
Received:
November 25, 2009
Revised:
July 29, 2010
Posted:
August 3, 2010
Published:
October 13, 2010
Online:
October 13, 2010
Citation
Chekchaki, M., Lazarus, V., and Frelat, J. (October 13, 2010). "Analytical and 3D Finite Element Study of the Deflection of an Elastic Cantilever Bilayer Plate." ASME. J. Appl. Mech. January 2011; 78(1): 011008. https://doi.org/10.1115/1.4002306
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