Large deformation of thin films and layered flat panels: Effects of gravity

A general theory is presented for the large deformation of thin films and l ayered flat panels in which gravitational forces have a marked influence on the evolution of curvature, shape and instability. Isotropic, linear elast ic deformation is considered with small: strains and moderate rotations. Th e thermomechanical properties of the layered material are allowed to vary t hrough the panel thickness so as to derive a general result for multilayers and graded materials. Explicit analytical expressions are derived for the critical curvature and the critical "effective load" at which curvature bif urcation occurs. The analysis considers square, circular and rectangular pa nels that are simply supported at three points, with the thin film on the p anel facing either up or down. A boundary layer analysis is presented for r ectangular panels specifically to examine the effect of panel shape on curv ature evolution and geometric stability. Computational simulations involvin g full three-dimensional hyperelastic formulations with large rotations and two-dimensional hyper elastic formulations with moderate rotations were us ed to assess the validity of the analytical results. Systematic experiments on the large deformation characteristics of flat glass panels with and wit hout silicon nitride thin film deposits were carried out to check the predi ctive capabilities of the theory. The trends predicted by the theory and it s quantitative predictions of bifurcation with and without thin film deposi ts on the panels were found to be in reasonable agreements with experiments . The limits of the solutions of the present theory for the special case of thin films on substrates with only mismatch strains are shown to converge to prior analytical results. Furthermore, the theory is shown to capture th e experimental trends observed during large deformation in thin-film/substr ate systems in the absence of gravitational effects. (C) 2001 Acta Material ia Inc. Published by Elsevier Science Ltd. All rights reserved.