Unexpected hardening effects in bilayered gel beams

A classical problem in structural mechanics is the evaluation of beam stretching and curvature in slender bilayered beams, due to mechanical actions, thermal distortions, differential growth, and more recently, to swelling. We investigate the non–monotonic changes in the curvature of swollen bilayer beams due to mismatches in physical properties of the two layers starting from a simple structural approach, and discuss the apparent contrast with the well–known Timoshenko’s formula through a scaling analysis. Due to the large strains involved in the problem, we also discuss the problem through a thermodynamics based on Gent model for the elastic contribution to the free–energy of the gels.