A three-dimensional theory has been established for the piezoresistivity of carbon nanotube (CNT) polymer composites. Based on the Mori-Tanaka method in meso-mechanics theory and considering quantum tunneling effect between CNTs, an approach to calculate equivalent electrical conductivity of composites was proposed. On this basis, a piezoresistive theory, which incorporates the effect of composites' geometric nonlinearity, was developed for CNT polymer composites. The theory is dependent only on some basic physical parameters of the materials. A finite element formula of the theory for the numerical calculation of piezoresistivity was presented from the analysis of both elastic and electric fields. Numerical simulations demonstrated that the results predicted by the theory were in good agreement with those of the experimental tests. Parameter sensitivity analysis revealed that when both the potential barrier height of the matrix and the initial average separation distance between CNTs increased, the piezoresistivity obviously increased. However, with the increase in aspect ratio and CNT conductivity, the piezoresistivity decreased gradually. A practical engineering application of this theory is also provided.
Keywords: carbon nanotubes; composites; electrical conductivity; finite element; piezoresistivity.