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

Abstract

A general theory is presented for the large deformation of thin films and layered flat panels in which gravitational forces have a marked influence on the evolution of curvature, shape and instability. Isotropic, linear elastic deformation is considered with small strains and moderate rotations. The thermomechanical properties of the layered material are allowed to vary through 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 bifurcation occurs. The analysis considers square, circular and rectangular panels that are simply supported at three points, with the thin film on the panel facing either up or down. A boundary layer analysis is presented for rectangular panels specifically to examine the effect of panel shape on curvature evolution and geometric stability. Computational simulations involving full three-dimensional hyperelastic formulations with large rotations and two-dimensional hyper elastic formulations with moderate rotations were used to assess the validity of the analytical results. Systematic experiments on the large deformation characteristics of flat glass panels with and without silicon nitride thin film deposits were carried out to check the predictive capabilities of the theory. The trends predicted by the theory and its quantitative predictions of bifurcation with and without thin film deposits 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 the experimental trends observed during large deformation in thin-film/substrate systems in the absence of gravitational effects.