Large deformation analysis of a gel using the complex variable element-free Galerkin method

Abstract

Deformation of a gel is a complicated multiphysical process involving the diffusion of solvent and the mechanical stretching of polymeric networks. This process leads to a mechanical and diffusional equilibrium after a certain period of evolution. Here we present a large deformation analysis of a gel in the equilibrium state under environmental triggers using the complex variable element-free Galerkin (CVEFG) method. The work mainly addresses the numerical challenges encountered while a gel in contact with a solvent deforms only with the geometric constraints but without any force boundary conditions (implying that the force column in the final standard algebraic equations equals zero) and emphasizes the implementation of a different CVEFG approach. The material model is based on the work of Hong et al. (2008) and incorporates our previous efforts in the numerical implementation. The discretized equation system is derived from the complex variable moving least squares approximation and the Galerkin method. The essential boundary conditions are imposed through the penalty method. The proposed approach is verified by the simulation of the swelling-induced large deformation and surface instability of a confined single gel layer.