Articulated surface wrinkling of a patterned film with periodic stiffness distribution on a compliant substrate

Articulated surface wrinkling patterns can be induced through the mechanical instability of patterned stiff films with periodic stiffness distributions (including periodic material and/or film thickness distributions) on a compliant substrate. To explore this articulated surface wrinkling, the governing equations are established by energy minimization, and the theoretical results are consistent with those from experiment and finite-element simulations. Morphology transitions from articulated wrinkling to trapezoidal or sine–trapezoid hybrid wrinkling are observed when the geometrical or material property parameters beyond a specific interval. Phase diagrams are established for the formation of articulated wrinkling morphology with respect to the geometrical and material parameters. The results show that articulated wrinkling is observed for a patterned film on a compliant substrate, depending on the periodic segment dimensions of the patterned film compared to the sinusoidal wrinkle wavelength of the corresponding homogeneous film. Compared to the sinusoidal wrinkling of a homogeneous film, articulated wrinkling has notably larger wrinkling wavelength and normal traction at the interface (approximately double when L₁=L₂), however, has slightly smaller amplitude and film strains (membrane and bending peak strains). This study is a good reference for designing articulated surfaces with potential applications in many areas, especially energy harvesting devices, because of the controlled deformation location and strain distribution of such surfaces.