Conformability of flexible sheets on spherical surfaces

Three-dimensional surface-conformable electronics is a burgeoning technology with potential applications in curved displays, bioelectronics, and biomimetics. Flexible electronics are notoriously difficult to fully conform to nondevelopable surfaces such as spheres. Although stretchable electronics can well conform to nondevelopable surfaces, they need to sacrifice pixel density for stretchability. Various empirical designs have been explored to improve the conformability of flexible electronics on spherical surfaces. However, no rational design guidelines exist. This study uses a combination of experimental, analytical, and numerical approaches to systematically investigate the conformability of both intact and partially cut circular sheets on spherical surfaces. Through the analysis of thin film buckling on curved surfaces, we identify a scaling law that predicts the conformability of flexible sheets on spherical surfaces. We also quantify the effects of radial slits on enhancing conformability and provide a practical guideline for using these slits to improve conformability from 40% to more than 90%.