Hydrogels are soft, hydrophilic materials which can absorb a large volume of solvent and undergo finite volumetric deformations known as swelling. The swelling of a hydrogel can be a driving mechanism for complex material responses such as pattern transformation which lead to change of periodicity as a result of a microscopic instability in periodic materials. In the present contribution, we deal with the computational analysis of swelling-induced instabilities in periodic hydrogels. The stability analysis based on the Bloch-Floquet theory is carried out within a transient two-field minimization-type variational principle. The presented formulation and methodology for the stability analysis are computationally efficient, since the computations are carried out on the smallest representative volume element of the microstructure. Within this framework, we study swelling-induced microscopic instabilities for various perforated hydrogels. Our findings are consistent with experimental observations and show that the so-called diamond plate patterns are the critical buckling mode for voided microstructures. Moreover, we observe long-wavelength instabilities for certain volume fractions of voids.
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