Closed-form solutions for the piezoresistivity properties of short-fiber reinforced composites with percolation-type behavior

Abstract

A new analytical formulation for the modeling of piezoresistive fiber-reinforced composites with percolation-type behavior is presented in this work. Firstly, we develop a closed-form solution of the electrical conductivity of oriented short-fiber reinforced composites by using generalized spherical harmonics series expansions of a Mori-Tanaka (MT) model. Piezoresistive effects are accounted for by means of three distinct mechanisms, namely filler reorientation, volume expansion, and breakage/formation of conductive paths. Then, this solution is used to derive simple analytical formulas to estimate the linear piezoresistivity coefficients. To illustrate the potentials of the proposed formulation, numerical results and discussion are presented on its application to the modeling of the piezoresistive composites doped with carbon nanotubes (CNTs). The presented formulation is also inlaid in a standard 3D finite element code to simulate the electromechanical response of full-scale CNT-based structural elements. The reported results demonstrate the capabilities of the proposed formulation to link the microstructural properties of short-fiber composites with the macroscopic response of structural systems with extraordinarily fast computation times and accuracy.