Adhesion-induced roof collapse of a rectangular micro-groove under applied pressure

In soft lithography roof collapse is frequently observed on the stamp surface consisting of rectangular micro-grooves which yields unwanted contact between the sagged surface and the substrate. Deep understanding of the adhesive contact behavior is a key to design of high-performance collapse-resistant stamp. Both theoretical and numerical studies are presented for a single rectangular micro-groove in the middle of the stamp surface under applied pressure. The JKR-type adhesion solution is established by the principle of superposition and equivalent energy release rate, with a series of closed-form expressions derived which are consistent with previous studies. Finite element analysis (FEA) is performed based on virtual crack closure technique (VCCT) to investigate the roof collapse mechanism with interfacial adhesion and applied pressure considered. Comparison of theoretical, numerical, and experimental results demonstrates that both size effect and constitutive nonlinearity of the stamp on the self-collapse contact width are not obvious for shallow grooves but become prominent for deep grooves, so that the obtained analytical solution is limited to shallow grooves due to its assumptions of half-plane and linear elasticity adopted for the stamp. For deep grooves, the present FEA method shows potential to capture more accurate results.