Millimeter-Wave Metamaterial-Based Strain Sensor Concept

We present a fully telemetric strain sensor concept based on a novel millimeter-wave metamaterial and show the experimental proof of concept. The metamaterial consists of a single layer of copper structures that are embedded between two sheets of thermoplastic polyurethane (TPU). Our metamaterial design specifically exploits the significant difference in elastic modulus between copper and TPU, so that the sensor effect does not require deformation of the copper structures. This prevents degradation due to delamination or cracking of the copper layer. The metamaterial is manufacturable with low-cost state-of-the-art manufacturing methods of conformable electronics. The geometrical parameters of the unit-cell structures are determined from finite-element simulations. We present a semi-analytical model of the sensor effect that allows for a low computational cost calculation of the sensitivity and provides a detailed analysis of the metamaterial unit-cell components in terms of their contribution to the sensitivity. Our model shows that the change in relative permittivity due to strain, an effect analogous to inverse electrostriction, contributes significantly to the sensitivity. We recorded the reflection spectra of a sample using millimeter-wave laboratory equipment and determined the sensitivity from the strain-induced shift of the characteristic minima in the reflection spectra. The experiment gives a sensitivity of 13117 ± 465 Hz/microstrain. The distinguishing features of our proposed sensor concept are the minimal strain-induced delamination due to negligible deformation of the metallic structures and that read-out is implemented in reflection which allows for the measurement of metal components.