Wrinkled structures have been widely used to accommodate large deformation through reversible geometric transformations. In this study, we investigate coupled wrinkling and bending in a strain-mismatched tri-layer structure composed of a thin film sandwiched between two pre-strained elastomeric substrates. Upon release of the pre-strain, mismatch-induced compressive stress leads to simultaneous global bending of the structure and localized wrinkling of the film. The bending curvature is governed by the thickness ratio of the substrates, while the onset of wrinkling is determined by the normalized film stiffness. A theoretical model based on energy minimization describes the bending curvature, and a linear buckling analysis provides the critical wrinkling condition. Experimental observations and finite element simulations show good agreement with the theoretical predictions. The results provide a mechanical framework for understanding and designing coupled bending-wrinkling behavior in multilayer soft structures.

Keywords: Wrinkling, Buckling instability, Multilayer structures, Bending curvature