Fractional description for the rate‐dependent viscoelastic response of tough hydrogels

Abstract Metal‐coordination mediated tough hydrogels have been considered as a promising materials for novel utilization in programmable actuation structures. However, the rate‐dependent mechanical behavior attributed to their intrinsic mechanical properties of mixed elasticity and viscosity, imposing a challenge for the realization of controllable deformations. In this work, the effect of stretch rate was incorporated into a variable fractional order model in order to describe and predict the rate‐dependent mechanical response of physically tough hydrogels. Firstly, we provide an iteration algorithm for model estimation and conduct simulations of the stress response under monotonic stretch to verify the applicability of proposed model. The performance of proposed model is compared with the existing model to validate its accuracy. Then, the present model is employed to describe the rate‐dependent stress response under cyclic loading. The change rule of related parameters with stretch rate is also unraveled by the present model, which is further utilized to test the model's predictive ability. Moreover, the physical meaning of variable order is qualitatively explored in conjunction with the evolution mechanism of dynamic bonds.