On the inverse determination of displacements, strains, and stresses in a carbon nanofiber/polyurethane nanocomposite from conductivity data obtained via electrical impedance tomography

Carbon nanofiller-modified composites possess extraordinary potential for structural health monitoring because they are piezoresistive and therefore self-sensing. To date, considerable work has been done to understand how strain affects nanocomposite conductivity and to utilize electrical impedance tomography for detecting strain or damage-induced conductivity changes. Merely detecting the occurrence of mechanical effects, however, does not realize the full potential of piezoresistive nanomaterials. Rather, knowing the mechanical state that results in the observed conductivity changes would be much more valuable from a structural health monitoring perspective. Herein, we make use of an analytical piezoresistivity model to inversely determine the displacement field of a strained carbon nanofiber/polyurethane nanocomposite from conductivity changes obtained via electrical impedance tomography. From the displacements, kinematic and constitutive relations are used to calculate strains and stresses, respectively. A commercial finite element simulation is then used to validate the accuracy of these predictions. These results concretely demonstrate that it is possible to inversely determine displacements, strains, and stresses from conductivity data thereby enabling unprecedented insight into the mechanical response of piezoresistive nanofiller-modified materials and structures.