Theoretical Model of the Island Effect in Flexible Electronics under Equal Biaxial Stretching

Island-bridge architecture represents a widely used structural design strategy in the field of stretchable inorganic electronics, where flexible serpentine interconnects function as bridges to accommodate most of the deformation, while the islands residing functional devices exhibit minimal deformation. The mismatch of Young's modulus between the elastic substrate and the rigid islands usually leads to stress concentration, which is named the island effect. This phenomenon can significantly increase the risk of interfacial damage, such as debonding and tearing failure near the island. In this work, the mechanical model of the island effect under equal biaxial stretching is developed based on theoretical analysis, simulation, and experimental measurement. The scaling law of the displacement and strain distributions on the substrate surface illustrates that the ratio of the island radius to the substrate length is the main controlling parameter of the island effect, proved by the experimental and numerical results. The criterion distinguishing whether the island effect problem is axisymmetric is derived from this. Further, the deformation field in periodic array structure is predicted based on the theoretical model, demonstrating its potential for application in flexible electronic devices.