Relaxation Dynamics of Capillary Folding of Thin Elastic Sheets with Pinned Contact Lines

Capillary folding is the process of folding planar objects into three-dimensional (3D) structures using capillary force. It has many important industrial applications, e.g. the fabrication of microelectromechanical systems. In this talk, we introduce a 3D model for the capillary folding of thin elastic sheets with pinned contact lines. The energy of the system consists of interfacial energies between the different phases, and the elastic energy given by the nonlinear Koiter's model which allows large deformations of the sheet. We derive the governing equations for the static system using a variational approach and develop a numerical method to find equilibrium solutions via a relaxation dynamics. Simulation results are in good agreement with the physical experiments. We present bifurcation diagrams for the folding of a triangular sheet, which exhibit rich and fully 3D behaviors not captured by previous 2D models. Our results provide new insights into the nonlinear process of capillary folding and the design of microfabrication techniques.