A numerical framework for two-dimensional large deformation of inhomogeneous swelling of gels using the improved complex variable element-free Galerkin method

A numerical framework based on the improved complex variable element-free Galerkin (ICVEFG) method is developed for large deformation analysis of inhomogeneous swelling of gels. In this work, a decomposed free-energy function is derived that avoids the difficulty of treating the chemical potential as a temperature-like variable by changing the chemical potential load into a mechanical load. The Galerkin weak form equation system is derived for inhomogeneous swelling of gels. The essential boundary conditions are imposed through the penalty method. This leads to the corresponding formulae of the improved complex variable moving least-squares (ICVMLS) approximation for 2-D large deformation inhomogeneous swelling of gels. Some example problems of inhomogeneous swelling induced behaviors such as wrinkling, crease and bifurcation are investigated using the developed ICVEFG framework.