  A cylindrical hydrogel tube, completely submerged in water, hydrates by
swelling and filling its internal cavity. When it comes back into contact with
air, it dehydrates: the tube thus expels the solvent through the walls,
shrinking. This dehydration process causes a depression in the tube cavity,
which can lead to circumferential buckling. Here we study the occurrence of
such buckling using a continuous model that combines non-linear elasticity with
Flory-Rehner theory, to take into account both the large deformations and the
active behavior of the hydrogel. In quasi-static approximation, we use the
incremental deformation formalism, extended to the chemo-mechanical equations,
to determine the threshold value of the enclosed volume at which buckling is
triggered. This critical value is found to depend on the shell thickness,
chemical potential and constitutive features. The results obtained are in good
agreement with the results of the finite element simulations of the complete
dynamic problem.

Soft Condensed Matter