Coupled field modeling of thermoresponsive hydrogels with upper/lower critical solution temperature

An inf–sup stable FE formulation for the thermo-chemo-mechanical simulation of thermoresponsive hydrogels is herein proposed by approximating the displacement field via quadratic shape functions and both the chemical potential (fluid pressure) and the temperature fields by linear functions. The formulation is implemented into a stable thermo-chemo-mechanical user-element subroutine (UEL) in Abaqus, denoted as Q2Q1Q1. The proposed formulation has been validated in relation to thermoresponsive hydrogels to interpret several examples of transient diffusion-driven swelling deformations. First, the upper/lower critical solution temperature behaviors of thermoresponsive hydrogels has been captured, studying several peculiarities comprising the diffusion length influence at the instantaneous loading state and the overlooked influence of the mass flux and the hyperelastic stretching on the temperature field. Subsequently, numerical analysis have been conducted in order to investigate the impact of temperature-dependent swelling ratio on the mechanical behavior of spheres undergoing compression. The accuracy of the proposed formulation has been assessed by numerically replicating the seminal experiments that explore the influence of crosslinking density on the thermally driven swelling of PNIPAAm hydrogels.