Conformability of a Thin Elastic Membrane Laminated on a Rigid Substrate With Corrugated Surface

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: 1) fully conformed, i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap; 2) partially conformed; and 3) nonconformed, i.e., the membrane remains flat if gravity is not concerned. Good conformability can enhance effective membrane-to-substrate adhesion and can facilitate heat/signal transfer across the interface, which are of great importance for micromembranes or nanomembranes transferred on target substrates and for flexible electronics laminated on rough biotissues. To reveal the governing parameters in this problem and to predict the conformability, energy minimization method is implemented with two different interfacial models, adhesion energy versus traction-separation relation. Depending on the complexity of the models, one to four dimensionless governing parameters have been identified to analytically predict the conformability status and the point of delamination if partial conformability is expected. In any case, partial conformability is achieved only when membrane energy is considered.