thin film plasticity

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.

Dear professor suo I am a master graduate of professor sun jun in xi'an jiaotong university, I have done some research on the tension of cu film on Pi substrate. I have a question about the mechanical behavior of thin film:the range of elastic deformation is enlarged just as the plastic stage in your simulation results, since the mutiple neckings result in improved plasticity of Pi-bonded Cu film.could you give me some advice? many thanks