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The object of this work is a numerical model aimed at predicting the electrical conductivity of polymeric matrices filled with Carbon Nano-Tubes (CNT). The model, developed within the GRAPSS, ”Graphene-Polymeric Spray Sensor for Shape Recognition of Super-Deformable Structures” a National Project entirely funded by CIRA, will be used to address the design of a sprayable sensor aimed at measuring large deformations. The phenomenon of the tunneling, at the basis of the electrical and thermal conductivity of CNT filled polymeric matrices, was modeled through the finite element, FE, approach. Each particle was schematized as a cluster of nodes connected by highly conductive elements, in compliance with the large conductivity of the CNTs. When the tunneling condition was verified between two particles, a link was realized; the specific electrical resistance was computed on the basis of parameters like the mutual distance and the tunnel cross section area. The resulting system, a truss-structure network contained within a reference cubic volume, was then solved through a thermal analogy. The inward and outward currents, passing through two opposite faces of the cube, were simulated by applying thermal fluxes of opposite sign; the voltage drop caused by the global resistance was then estimated through a steady heat transfer analysis, giving the temperature gradient between the opposite faces. The ratio between the voltage drop and the inward-upward current (respectively, the temperature and the heat flux) represented then the global resistance of the cube. A parametric investigation was finally performed, finding out the dependence of the gage factor (strain vs resistance variation) on CNT concentration and aspect ratio parameters (curvature, diameter-length ratio) and the electrical conductivity.
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