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

Yihui Zhang, Haoran Fu, Sheng Xu, Jonathan A. Fan, Keh Chih Hwang, Jianqun Jiang, John A. Rogers, Yonggang Huang*

*Corresponding author for this work

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)115-130
Number of pages16
JournalJournal of the Mechanics and Physics of Solids
Volume72
DOIs
StatePublished - Dec 1 2014

Fingerprint

Fractals
fractals
Electronic equipment
antennas
Antennas
Electrodes
electrodes
wiring
Electric wiring
Magnetic resonance
electronics
visibility
layouts
Stretching
magnetic resonance
Imaging techniques
microstructure
Microstructure
predictions
Experiments

Keywords

  • Fractal interconnects
  • Hierarchical computational model
  • Ordered unraveling
  • Postbuckling

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Zhang, Yihui ; Fu, Haoran ; Xu, Sheng ; Fan, Jonathan A. ; Hwang, Keh Chih ; Jiang, Jianqun ; Rogers, John A. ; Huang, Yonggang. / A hierarchical computational model for stretchable interconnects with fractal-inspired designs. In: Journal of the Mechanics and Physics of Solids. 2014 ; Vol. 72. pp. 115-130.
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A hierarchical computational model for stretchable interconnects with fractal-inspired designs. / Zhang, Yihui; Fu, Haoran; Xu, Sheng; Fan, Jonathan A.; Hwang, Keh Chih; Jiang, Jianqun; Rogers, John A.; Huang, Yonggang.

In: Journal of the Mechanics and Physics of Solids, Vol. 72, 01.12.2014, p. 115-130.

Research output: Contribution to journalArticle

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