A facile, robust and versatile finite element implementation to study the time-dependent behaviors of responsive gels

Though there are significant efforts to develop numerical platforms to simulate the dynamic behaviors of responsive gels, several challenges were not successfully resolved, including truly robust method to handle time-dependent and coupled mass diffusion and deformation fields particularly at very short-time and complicated instability. In this Letter, a facile, robust and versatile finite element method was developed to resolve these challenges by adopting ramping boundary conditions, viscous damping, and damped Newton-Raphson method. This method can be readily implemented in a commercial platform COMSOL Multiphysics. The finite element method was showcased to study several dynamic examples that possess very short-time surface wrinkles, wrinkle evolutions, and incorporation with other physics field. Given the fact that the implementation is through a commercial platform, this method can have significant contributions to the studies of gels.