The CNT-PDMS composite has been widely adopted in flexible devices due to its high elasticity, piezoresistivity, and biocompatibility. In a wide range of applications, CNT-PDMS composite sensors were used for resistive strain measurement. Accordingly, the percolation threshold 2%~4% of the CNT weight ratio in the CNT-PDMS composite was commonly selected, which is expected to achieve the optimized piezoresistive sensitivity. However, the linear range around the percolation threshold weight ratio (2%~4%) limits its application in a stable output of large strain (>20%). Therefore, comprehensive understanding of the electromechanical, mechanical, and electrical properties for the CNT-PDMS composite with different CNT weight ratios was expected. In this paper, a systematic study was conducted on the piezoresistivity, Young’s modulus, conductivity, impedance, and the cross-section morphology of different CNT weight ratios (1 to 10 wt%) of the CNT-PDMS composite material. It was experimentally observed that the piezo-resistive sensitivity of CNT-PDMS negatively correlated with the increase in the CNT weight ratio. However, the electrical conductivity, Young’s modulus, tensile strength, and the linear range of piezoresistive response of the CNT-PDMS composite positively correlated with the increase in CNT weight ratio. Furthermore, the mechanism of these phenomena was analyzed through the cross-section morphology of the CNT-PDMS composite material by using SEM imaging. From this analysis, a guideline was proposed for large strain (40%) measurement applications (e.g., motion monitoring of the human body of the finger, arm, foot, etc.), the CNT weight ratio 8 wt% was suggested to achieve the best piezoresistive sensitivity in the linear range.

In flexoelectricity, a strain gradient can induce polarization and a polarization gradient can induce mechanical stress. In this paper, in order to identify the contributions of each strain gradient component, the flexoelectric theory is reformulated by splitting the strain gradient tensor into mutually independent parts. Two sets of orthogonal higher-order deformation metrics are inherited and perfected to reformulate the internal energy density for isotropic materials. The deviatoric stretch gradient and the symmetric part of the rotation gradient are proved to disappear in the coupling of strain gradient to polarization and, moreover, the independent higher-order constants associated with the coupling of strain gradient to strain gradient reduce from five to three. The constitutive relations are then reformulated in terms of the new deformation and electric field metrics, and the governing equations and boundary conditions are derived according to the variational principle of electric enthalpy. On the basis of the present simplified flexoelectric theory, a flexoelectric Bernoulli–Euler beam theory is specified. Solutions for a cantilever subjected to a force at the free end and a voltage cross the thickness are constructed and the size-dependent direct and inverse flexoelectric effects are captured.