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.