Modeling and design of the self-twisting of hydrogel bilayer strips Authors: Jiayu Liu, Jingkai Guo, Tanvi Shroff, ChangKyu Yoon, David Gracias {\&} Thao D Nguyen

Self-folding of hydrogels via heterogeneous swelling can be used to create complex, 3D structures. A bilayer structure with a thermo-responsive hydrogel layer, that swells with decreasing temperature, and a non-swelling layer can respond to a temperature change by either bending into a ring or twisting into a helix. The equilibrium structure depends on the thickness ratio of the two layers, the ratio of the width to thickness of the bilayer, as well as the stiffness of the two layers and equilibrium swelling ratio of the hydrogel.~ These parameters can be controlled using lithographic photopatterning and multilayer deposition techniques.~ To guide the design of the bilayer structures, we developed a finite element model of the bilayer structure. The constitutive model of the hydrogel is described by a free energy density that includes a quasi-incompressible Neo-Hookean component~for the strain energy density of the polymer network and a Flory-Huggins component for the~free-energy density of mixing of the polymer and solvent. We discussed how variations in the layer thickness, slenderness, stiffness, and equilibrium swelling ratio can be used to design self-folded rings of different curvatures and helices with different helix angle and diameters.