Conformal Theoretical Modeling of Arbitrary Shape Flexible Electronic Sensors Mounted Onto General Curved Surface Substrates

Abstract Stretchable and flexible electronic sensors have been attracted to novel applications due to their conformal integration onto complex curved surfaces, whereas the mounting strains generated by the geometric mismatch of substrate surface and electronic sensors may cause non-conformal contact at the interface, thus would induce non-negligible effects on the performance of sensors. To investigate the influence rules of the shape of electronic sensors and their geometric parameters on conformal contacts, this paper presents a novel conformal model to study the arbitrary shaped films as flexible sensors mounted onto general curved-surface substrates. The energy minimization principle and the integral summation method play vital roles during the modeling, and three types of films with various shapes including rectangular, oval, and hexagonal mounted onto a bicurvature substrate are investigated. The influences of three dimensionless shape parameters of oval and hexagonal film/substrate contacts are analyzed for the dimensionless strain energy of conformal mounting. The strain and critical dimensionless strain energy of three films/bicurvature substrate contacts are calculated and compared under the same conformal area. The results demonstrated that the contour shape of electronic sensor has a considerable effect on conformal mounting and strain. Thus, the developed conformal model would have great significance in guiding the design of flexible electronic devices and sensors when applied to general curved surfaces.