Carbon nanofiller-modified composites have incredible potential for self-sensing and structural health monitoring (SHM) because they are piezoresistive. That is, the electrical conductivity of a nanocomposite is inherently coupled with mechanical perturbations such as damage and strain. Because of the correspondence of strain and damage with conductivity changes, non-invasive conductivity imaging techniques such as electrical impedance tomography (EIT) can enable unprecedented insight into the mechanical state of a nanofiller-modified composite. Furthermore, because of the potential of nanocomposites for self-sensing and SHM, considerable effort has been dedicated to studying the effect of strain on nanocomposite conductivity. That is, these efforts seek to determine the change in conductivity of a nanocomposite for a prescribed strain. However, from a SHM perspective, knowing the inverse relation would be much more useful. In other words, for an observed conductivity change, what is the underlying strain state? In light of the potential of EIT to provide insight into the conductivity distribution of a strained nanocomposite, we herein develop a method of estimating the infinitesimal strain tensor of a piezoresistive nanocomposite for observed conductivity changes. This is done by formulating an inverse problem that seeks to minimize the difference between an observed conductivity and a piezoresistivity model that predicts nanocomposite conductivity as a function of the strain in the least-squares sense. Next, this approach is specialized to the finite element method such that the nodal displacements giving rise to an observed conductivity change can be ascertained. Lastly, this method is tested analytically with noisy data. It is found that the proposed method can accurately reproduce nodal displacements and therefore strains from conductivity data.

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