dynamic bending stress analysis in sandwich thin film structure

Hello,

Does anybody know if there exists an analytical solution for stress distribution in a sandwich like/ multilayered thin films subjected to cyclic bending? The sandwich has line-patterned metal of submicrons in thick and a few microns in width, which was coated/deposited by other material on top and bottom (surrounding as well) with different thickness up to 20 microns.

We need to know minimum curvature without failure. I tried google and sciencedirect a little while, and Freund's thin film book... FEM analysis is an option here, though.

Thanks,