Modeling and Measurement of Permittivity Variation Under Compressing or Stretching for Flexible Composite Materials in X-Band

Flexible composite materials (FCMs) are promising materials for flexible microwave devices for emerging applications such as satellite communication in
${X}$
-band. The high-frequency dielectric properties of FCMs are the key property in the design. At the same time, to fully use the material flexibility, it is significant to know how the complex permittivity changes under different mechanical deformations. The high-frequency complex permittivity measurement itself is, however, difficult, not to mention the measurement under deformation; moreover, most studies consider the bending deformation only, but compressing/stretching may be more common. Combining the modified Debye model with the multicomponent unified mixing rule, this article proposes a prediction formula for the relative complex permittivity of FCMs under compressing/stretching deformation. A measurement approach based on the coaxial transmission/reflection (T/R) method was demonstrated. The carbon black/polydimethylsiloxane (CB/PDMS) samples with different doping concentrations (0 wt%, 1.8 wt%, 3.5 wt%, and 5.2 wt%) were taken as the FCM example. The experimental and theoretical results of 5.2 wt% CB/PDMS under 11.83% vertical compression in the
${X}$
-band were in good agreement. A stretchable absorber was further fabricated and tested based on the FCM, and the measured absorption spectra before and after stretching agreed well with the theoretical prediction.