A hierarchical computational model for stretchable interconnects with fractal-inspired designs

Stretchable electronics that require functional components with high areal coverages, antennas with small sizes and/or electrodes with invisibility under magnetic resonance imaging can benefit from the use of electrical wiring constructs that adopt fractal inspired layouts. Due to the complex and diverse microstructures inherent in high order interconnects/electrodes/antennas with such designs, traditional non-linear postbuckling analyses based on conventional finite element analyses (FEA) can be cumbersome and time-consuming. Here, we introduce a hierarchical computational model (HCM) based on the mechanism of ordered unraveling for postbuckling analysis of fractal inspired interconnects, in designs previously referred to as 'self-similar', under stretching. The model reduces the computational efforts of traditional approaches by many orders of magnitude, but with accurate predictions, as validated by experiments and FEA. As the fractal order increases from 1 to 4, the elastic stretchability can be enhanced by ~200 times, clearly illustrating the advantage of simple concepts in fractal design. These results, and the model in general, can be exploited in the development of optimal designs in wide ranging classes of stretchable electronics systems.