A mixed isogeometric analysis approach for the transient swelling of hydrogel

Abstract In this paper, a mixed isogeometric analysis approach is developed to realize accurate and efficient simulations of the transient swelling of hydrogel strongly coupled with large deformation and fluid diffusion. In this method, the mixed isogeometric element is presented for the coupled multi-physics problems accompanied with the volumetric locking caused by the incompressibility of polymeric chains and solvent molecules. Such type of element is based on the subdivision properties of the Non-Uniform Rational B-Spline (NURBS) basis functions, in which the fine and coarse basis functions with the same order are used to discretize the displacement and chemical potential fields, respectively. Meanwhile, an auxiliary configuration for the multiplicative decomposition of deformation gradient is introduced to eliminate the difficulty due to certain specific cases, such as a negative infinite chemical potential for the hydrogel in a dry state. Then, the virtual work equations are derived based on the strain energy function with the ability of describing the constitutive relation of the hydrogel for large deformation from any swollen state and the mass conservation. The discrete formulations of the linearized virtual work equations for two fields on the base of the mixed isogeometric element are obtained. The efficiency, accuracy and validity of the proposed mixed isogeometric analysis approach are illustrated by solving several representative problems. The applicability of the proposed method is further demonstrated through two practical applications, which indicates that it has great potential to serve as an effective numerical tool for mechanical analysis and design of many hydrogel-based bionic devices.