An analytical mechanics model for the island-bridge structure of stretchable electronics

In stretchable electronics, the island-bridge structure on a soft substrate plays an important role in achieving large stretchability. A key issue in developing such a system is to prevent the island-bridge structure from breaking during use because it is composed of brittle semiconductor materials (e.g., silicon) which withstand very small strains (∼1%). In the following, an analytical mechanics model of the island-bridge structure is established and the accurate solution is obtained. A validated scaling law is found to reveal the dependence of the normalized maximum strain in the island on the prestrain of the substrate, which controls the mechanical failure of the island-bridge structure and provides a theoretical basis for fracture-safe design of stretchable electronics.