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Analysis of electrical resistance changes in liquid metal printed wires under strain for stretchable electronics

Eutectic gallium–indium (eGaIn) is an electrically conductive metal that is liquid at room temperature and has been used for electrical wires in a variety of stretchable electronics. However, only tensile directional and tensile-vertical eGaIn wires have been analyzed in detail with regard to their resistance changes under tension, limiting the ability to precisely predict and adjust resistance changes in eGaIn-based electronics. To overcome these limitations, this study formulated and validated models for prediction of the resistance changes in tilted and circular arc-shaped eGaIn wires under uniaxial strain. In tensile tests, the prediction models showed not only changes in resistance highly similar to the actual resistance changes in the strain range from 0% to 150% with root mean square errors of less than 0.05 between the predicted and measured resistance changes, but also adjustability of the resistance changes under tension according to the initial tilt angle of the tilted eGaIn wires or initial shape of arc eGaIn wires. Additionally, the prediction models developed and applied for eGaIn-based applications, including eGaIn strain sensors, heaters, and stretchable wires, yielded accurate predictions. The proposed models are expected to be useful for the precise prediction of resistance changes and pattering of eGaIn-based stretchable electronics.