Self-sensing nanocomposites hold immense potential for structural health monitoring (SHM) because their electrical conductivity is influenced by mechanical effects such as strain and damage. This property, known as piezoresistivity, has been leveraged by numerous researchers for damage detection. However, from a SHM perspective, it would be much more beneficial to know the stresses that precipitate failure so that mitigating actions can be taken. Herein, we propose a novel method of accomplishing this based on the concept of piezoresistive inversion. Using simulations, the conductivity of a deformed piezoresistive nanocomposite is first determined using electrical impedance tomography (EIT). Next, the piezoresistive inversion process is used to determine the displacement field that gives rise to the conductivity obtained via EIT. Strains are then determined from kinematic relations and stresses from constitutive relations. A suitable failure criterion is then used to predict the location and likelihood of failure. Using these simulations, we demonstrate that the proposed approach allows for the accurate localization and quantification of stress concentrations which may induce failure. Because of these damage prediction capabilities, this approach has the potential to enable unparalleled predictive SHM capabilities.