A Peano-Gosper Fractal-Inspired Stretchable Electrode with Integrated Three-Directional Strain and Normal Pressure Sensing

A novel stretchable flexible electrode capable of simultaneously detecting isotropic three-directional strain and normal pressure has been developed. Inspired by the recursive symmetry of the Peano-Gosper fractal, the electrode integrates liquid metal (EGaIn) microchannels within a PDMS matrix to achieve uniform strain distribution and mechanically robust conductive pathways under large deformation. Within a strain range of 0–60%, the electrode exhibits highly consistent three-directional responses, with resistance variation across axes kept below 4% and a gauge factor (<i>GF</i>) standard deviation of only 0.0252. The device demonstrates low hysteresis (minimum DH = 0.94%), good cyclic durability, and reliable electromechanical stability. For normal pressure sensing (0–20 kPa), it provides a linear response (<i>R</i>² ≈ 0.99) with a moderate sensitivity of 0.198 kPa⁻¹. Wearable tests on the wrist, finger, and fingertip confirm the electrode’s reliable operation in multidimensional mechanical monitoring. This integrated fractal–liquid metal design offers a promising route for multifunctional sensing in applications such as soft robotics, human–machine interaction, and wearable electronics.