An improved interpolating complex variable element free Galerkin method for the pattern transformation of hydrogel

Abstract

In this paper, an effective interpolating complex variable element free Galerkin method is proposed for the steady large deformation analysis of hydrogels. In this meshless method, the essential boundary conditions can be applied directly without using other special methods, which leads to less unknown coefficients. Through computing the swelling large deformation of a square hydrogel with three constrained boundaries, the presented meshless method is validated with higher accuracy and efficiency than other non-interpolating meshless methods. Based on the developed meshless method, different samples with elliptical, circular and square holes in a square hydrogel are simulated for analyzing the pattern transformation. The numerical results indicate that the shapes and initial sizes of holes in hydrogels lead to different pattern transformation rules, actuating behaviors and area reductions of holes. Finally, according to the new findings, the potential applications of a square hydrogel are discussed by designing different shapes and initial sizes of holes.