Buckling of thin gel strip under swelling

- An analytical model is established for the swelling-induced buckling of a thin gel strip.
- The closed-form solutions for the amplitude and wavelength are obtained.
- The results provide design guidelines for the buckled configuration quantitatively.

The buckling of thin gel film has attracted much attention due to its applications in the design of three-dimensional structure from two-dimensional template. We have established an analytical model to study the swelling-induced buckling of a thin gel strip with one edge clamped and the others free. The closed-form solutions for the amplitude and wavelength of the buckled shape are obtained by energy minimization of the total potential energy. The analytical results agree well with finite element analysis based on the inhomogeneous gel theory without any parameter fitting. The model provides a route to study complex postbuckling behaviors of thin gel films and guidelines to design the buckled configuration quantitatively by controlling the swelling ratio.