Eigenvalue Buckling Analysis of Swelling-Induced Pattern Transformation in Porous Gel Films

Abstract

In this study, we perform finite element analysis of swelling-induced pattern transformation in porous gel films. An inhomogeneous field theory for polymeric gels is implemented as a user-defined material subroutine into a commercial finite element package. Swelling process is analyzed by increasing the chemical potential of external solvent. To investigate the point of buckling and the buckling mode, eigenvalue buckling prediction is conducted using a quasi incremental loading pattern instead of using the chemical potential, because the chemical potential is not available in eigenvalue buckling analysis. This approach is verified by analyzing pattern transformation in gel films with a square lattice of holes. It is found that diamond plate patterns are successfully predicted regardless of including an increase of the chemical potential under the base state, while as the base state departs from the buckling point, the buckling stress is underestimated, especially in this study, by up to about 40%. It is further found that diamond plate patterns are the most dominant mode as a result of using a larger periodic unit.