Nonlinear stretching mechanics of planar Archimedean-spiral interconnects for flexible electronics

Stretchable island-bridge structures are widely used in flexible inorganic electronics. The recently proposed Archimedean-spiral interconnects are good candidates for achieving a high level of stretchability. The optimal design of the Archimedean spiral depends on systematic exploration of the geometric variables, which is still lacking in theoretical fundamentals. In this work, a theoretical model for the mechanical responses of Archimedean-spiral interconnects under the in-plane stretching is developed based on the finite deformation plane-strain beam theory. The key parameters of the mechanical responses including the effective tensile stress, maximum strain and deformed configurations are analytically derived and validated by finite element analysis for a wide range of geometric variables. The theoretical and numerical results demonstrate that the stress-strain responses and elastic stretchability can be well tailored by three nondimensionless variables. Quantitative comparison shows that the Archimedean-spiral interconnects may have certain advantage over the widely-adopted serpentine interconnects. The results obtained in this work are beneficial for facilitating ultra-stretchable spiral interconnects for future stretchable electronics.