Geometry-Encoded Soft Strain Sensing via Liquid-Metal Transmission Lines

Reliable strain sensing in soft systems remains challenging under mechanically complex conditions, where compression, folding, transverse deformation, and environmental perturbations often interfere with tensile-strain readout. Existing flexible strain sensors typically rely on amplitude-based electrical responses and therefore frequently require calibration, compensation, or signal reconstruction to isolate axial deformation. Here, we present a soft liquid-metal transmission-line sensor that directly encodes axial elongation into the time-of-flight of an electromagnetic pulse. Because the readout is governed by the total propagation path length, deformation modes that do not alter this path-including localized compression, folding, and biaxial transverse strain-produce negligible influence on the measured signal. The sensor exhibits linear strain response over a wide working range up to 400% strain, together with a strain-range-independent length resolution of 10 mm. Owing to its geometry-governed mechanism, the device enables self-referenced and calibration-free strain measurement with strong inter-device consistency, while maintaining stable operation under large pre-strain, cyclic loading, and irreversible deformation. Reliable sensing is further demonstrated on curved surfaces, wearable systems, inflatable structures, pneumatic artificial muscles, and task-level clinical tourniquet monitoring under dynamically varying deformation conditions. This work provides a robust and reconstruction-free strategy for strain sensing in soft electronics, wearable systems, and clinical healthcare.