Anisotropic swelling of thin gel sheets

We describe the anisotropic swelling within the Flory--Rehner thermodynamic model through an extension of the elastic component 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 different 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.