Finite bending solutions for layered gel beams

We investigate the swelling–induced bending of a gel bilayer beam with homogeneous beam–like components, when the beam is embedded in a solvent bath of assigned chemical potential. We set the problem within the limits of finite elasticity with large distortions, with these latter determined via chemical equilibrium, by the elastic modulus of the gel, the chemical potential of the bath and the solvent–gel interaction parameter. We borrow our method of solution from finite bending of soft and incompressible beams, and get a non dimensional nonlinear equation governing the solution of the problem, whose solution is validated through a campaign of numerical experiments based on a complete stress–diffusion model.