A Thin Elastic Membrane Conformed to a Soft and Rough Substrate Subjected to Stretching/Compression

Conformability of bio-integrated electronics to soft and microscopically rough biotissues can enhance effective electronics-tissue interface adhesion and can facilitate signal/ heat/mass transfer across the interface. When biotissues deform, for example, when skin stretches or heart beats, the deformation may lead to changes in conformability. Although a theory concerning just full conformability (FC) under deformation has been developed (i.e., the FC theory), there is no available theory for partially conformable (PC) systems subjected to deformation. Taking advantage of the path-independent feature of elastic deformation, we find that the total energy of a PC system subjected to stretching or compression can be analytically expressed and minimized. We discover that the FC theory is not sufficient in predicting FC and a full energy landscape obtained by our PC theory is needed for searching for the equilibrium. Our results reveal that stretching enhances conformability while compression degrades it. In addition to predicting the critical parameters to maintain FC under deformation, our PC theory can also be applied to predict the critical compressive strain beyond which FC is lost. Our theory has been validated by laminating poly(methyl methacrylate) (PMMA) membranes of different thicknesses on human skin and inducing skin deformation.