Buckling patterns of thin films on compliant substrates: the effect of plasticity

Most previous studies on spontaneous buckling pattern formations in thin films on compliant substrates were limited to elastic deformation, where the herringbone mode is the most often observed under equi-biaxial compression. In practice, plastic deformation is often encountered in ductile metal and polymer films. The effect of plasticity on buckling patterns is explored in this paper using extensive finite element simulations, where the film is assumed to be elastic-perfectly plastic. It is found that upon equi-biaxial compression, depending on the competition among the yield strain, critical buckling strain and applied strain, three new types of patterns may emerge: the plastic diamond-like pattern, the elastoplastic square lattice pattern and the elastoplastic sharp herringbone pattern, and their characteristics are compared with the elastic herringbone mode. Moreover, unique features including the asymmetry in crests and troughs, the sharp saw-like undulation profile and varying wavelengths with applied strain are observed for some types of the new patterns. The study may find its potential applications in the design of stretchable electronics, fabrication of micro/nanofluid channels or channel networks, and morphogenesis of tissues and plants, among others.The study is supported by the National Natural Science Foundation of China (50928601), the National Science Foundation CMMI-CAREER-0643726, the World Class University program through the National Research Foundation of Korea (R32-2008-000-20042-0), the Chang Jiang Scholar Program of the Ministry of Education of China, and the Robert M and Mary Haythomthwaite Foundation