A coupled electro-mechanical FE approach was developed to investigate the piezoresistive response of carbon nanotube polymer composites. Gauge factors (GFs) and resistance variations of CNT–polymer composite systems were obtained by coupling Maxwell equations to mechanical loads and deformations through initial piezoresistive coefficients of the CNTs, the epoxy, and the tunnel regions, for different arrangements, percolated paths, tunnel distances, and tensile, compressive, and bending loading conditions. A scaling relation between GFs and applied strains was obtained to understand how variations in loading conditions and CNT arrangements affect sensing capabilities and piezoresistive carbon nanotube polymer composite behavior. These variations in GFs were then used to understand how the coupled strains, stresses and current densities vary for aligned and percolated paths for the different loading conditions, CNT arrangements, and tunnel distances. For the percolated path under tensile loading conditions, elastic strains as high as 16% and electrical conductivities that were four orders in magnitude greater than the initial matrix conductivity were obtained. Results for the three loading conditions clearly demonstrate that electrical conductivity and sensing capabilities can be optimized as a function of percolation paths, tunneling distance, orientation, and loading conditions for piezoresistive applications with large elastic strains and conductivities.
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