Substantial curvature effects on compliant serpentine mechanics

Serpentine interconnects (serpentines) with various degrees of curvature are often designed to absorb deformations and protect brittle active components in flexible devices. Serpentines with small curvature are modelled well using the traditional theory for doing so, but this overestimates the stretchability of serpentines with large curvature (e.g. the relative error exceeds 90%). Proposed here is a novel theoretical model in which a non-buckling serpentine is characterized as a large-curvature beam. Analytical solutions are derived, and systematic experiments and numerical simulations are reported to validate the accuracy and investigate geometrical dependence. It is found that (i) dimensionless geometrical parameters regulate the compliant mechanics of a serpentine, (ii) there is a certain arc angle that produces abnormal stretchability (i.e. the normalized stretchability is less than unity) and (iii) the flexibility and stretchability can be enhanced by between two and five orders of magnitude. This work offers a new way to construct optimal serpentine ribbons with large curvature for various applications.