The aim of this work is to develop a model to continuously predict inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(N-isopropylacrylamide) hydrogels. Employing this model, some benchmark homogeneous problems such as free, unidirectional constrained and biaxial constrained swelling as well as swelling of core-shell structures are investigated. The main advantage of the model is its ability to solve inhomogeneous deformations due to a stable behavior in the vicinity of the phase transition temperature. Therefore, inhomogeneous swelling of a spherical shell on a hard core with application to microfluidics is analytically and numerically investigated for various thicknesses of the shell. Based on the solved examples, it is shown that the model possesses continuity and stability in the vicinity of the phase transition temperature.
