Anisotropic swelling in thin gel sheets

We describe the anisotropic swelling within the Flory–Rehner thermodynamic model through an extension of the elastic com- ponent of the free–energy, which takes into account the oriented hampering of the swelling–induced deformations due to the presence of stiffer fibers. We also characterize the homogeneous free–swelling solutions of the corresponding anisotropic stress– diffusion problem, and discuss an asymptotic approximation of the key equations, which allows to explicitly derive the anisotropic solution of the problem. We propose a proof–of–concept of our model, realizing thin bilayered gel sheets with layers having dif- ferent anisotropic structures. In particular, for seedpod–like sheets, we observe and quantitatively measure the helicoid versus ribbon transition determined by the aspect ratio of the composite sheet.