Sectors such as the aerospace, civil, and automotive industries have experienced increasing demands and applications of fiber-reinforced composites. However, due to their nature of complex and often outwardly invisible failure modes, monitoring fiber-reinforced composites by non-destructive means is important. One way of monitoring these materials is by integrating self-sensing capabilities into the composites through nanofiller modification in order to make use of the piezoresistive effect. In this approach, changes in electrical resistivity are a function of mechanical strains, thereby allowing for intrinsic self-sensing. So far, predictive modeling work in this area has focused predominantly on microscale piezoresistivity. Much less work has considered the effect of the continuous fiber reinforcement, and research on achieving meaningful analytical predictions of resistivity changes in fiber-matrix material systems has been limited. Therefore, to overcome this gap, an analytical model that allows for predicting changes in the resistivity of a material system consisting of both a nanofiller-modified polymer phase and a continuous fiber reinforcement phase is presented. This approach is predicated on the development of an electrical concentric cylindrical model. We start by identifying our analysis domain: concentric cylinders representing a continuous reinforcing fiber surrounded by the nanofiller-modified matrix. Then, by enforcing the law of conservation of electrical charge and by utilizing existent piezoresistivity relations for the nanofiller-modified matrix, the system is homogenized in order to predict the change in the resistivity of the concentric cylinder as a function of applied strains and constituent properties. It is hoped that this preliminary result will be an important building block towards the development of a laminate theory of piezoresistivity.

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