Auxetics are mechanical metamaterials with the unique properties of expanding their transversal section upon longitudinal positive strain, decoupling the deformations in normal and transversal directions. Such property can be exploited to develop soft sensors that can provide feedback to different mechanical stimuli, e.g. pressure and shear force. In this work, we propose for the first time a mathematical model to analytically simulate and design the auxetic behavior in a capacitive strain gauge, and show that, for a polyurethane (PU) auxetic foam, Poisson Ratio's values can satisfy the negative gauge factor (GF) condition. We develop an innovative thermo-compressive process to obtain anisotropic auxetic PU sponges both in normal and normal/radial directions, and their mechanical properties are in agreement with the theoretical calculations validating our model. Then, we develop a capacitive strain gauge by integrating a normal auxetic PU foam with polydimethylsiloxane /carbon nanotubes electrodes. Results show that the capacitive change caused by an external force, is proportional to the induced deformation, but importantly it is also dependent on the direction of the applied force. A negative GF of GF = -2.8 is obtained for a longitudinal strain range up to 10%. This auxetic foam structure guarantees flexibility and paves the way for an improved design freedom for multimodal mechanical soft sensors providing new opportunities towards smart wearables and perceptive soft robots.
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