A generalized decoupling numerical framework for polymeric gels and its element-free implementation

Coupled diffusion of solvent molecules and mechanical stretching of polymeric networks induced swelling/deswelling in polymeric gels contributes to the ability of its "smart response" and "environmental sensitivity." In this article, the coupled diffusion and large deformation of polymeric gels are clarified into three kinds of deformation conditions which all involve swelling/deswelling. The real numerical challenge is identified for simulating swelling/deswelling induced deformation of gels by solving the partial deferential control equation of a popular monophase model for gels in steady equilibrium state with a standard process of numerical discretization. To address the numerical challenge, a generalized decoupling numerical framework is developed based on a multiplicative decomposition of deformation gradient. The proposed framework is more flexible and works for almost all cases of deformation of gels no matter involving swelling/deswelling or not. Its element-free implementation is also developed using the element-free IMLS-Ritz method and is validated through analyzing the three-dimensional stable and unstable large deformation of the constrained gel cube and tube.