A phenomenological model for shakedown of tough hydrogels under cyclic loads

Most tough hydrogels suffer accumulated damages under cyclic loads. The damages may stem from breakage of covalent bonds, unzipping of ionic crosslinks, or desorption of polymer chains from nanoparticle surfaces. Recent experiments report that when a tough hydrogel is subject to cyclic loads, the stress-stretch curves of tough hydrogels change cycle by cycle and approach a steady-state after thousands of cycles, denoted as the shakedown phenomenon. In this paper, we develop a phenomenological model to describe the shakedown of tough hydrogels under prolonged cyclic loads for the first time. We specify a new evolution law of damage variable in multiple cycles, motivated by the experimental observations. We synthesize nanocomposite hydrogels and conduct the cyclic tests. Our model fits the experimental data remarkably well, including the features of Mullins effect, residual stretch and shakedown. Our model is capable of predicting the stress-stretch behavior of subsequent thousands of cycles by using the fitting parameters from the first and second cycle. We further apply the model to polyacrylamide (PAAM)/poly(2-acrylanmido-2-methyl-1-propanesulfonic acid) (PAMPS) and PAAM/alginate double-network hydrogels. Good agreement between theoretical prediction and experimental data is also achieved. The model is hoped to serve as a tool to probe the complex nature of tough hydrogels, through cyclic loads.