Mechanics of stretchable electronics with high fill factors

Mechanics models are developed for an imbricate scale design for stretchable and flexible electronics to achieve both mechanical stretchability and high fill factors (e.g., full, 100% areal coverage). The critical conditions for self collapse of scales and scale contact give analytically the maximum and minimum widths of scales, which are important to the scale design. The maximum strain in scales is obtained analytically, and has a simple upper bound of 3tscale/(4ρ) in terms of the scale thickness tscale and bending radius ρ.