On the Development of Tensorial Deformation-Resistivity Constitutive Relations in Conductive Nanofiller-Modified Composites

Abstract

Polymers modified with conductive nanofillers have recently received considerable attention from the research community because of their deformation-dependent electrical resistivity. Known as piezoresistivity, this self-sensing capacity of nanocomposites has much potential for structural health monitoring (SHM). However, making effective use of the piezoresistive effect for SHM necessitates having a good understanding of the deformation-resistivity change relationship in these materials. While much insightful work has been done to model and predict the piezoresistive effect, many existing models suffer from important limitations such as being limited to microscales, over-predicting piezoresistive responses, and not considering complex deformations. We herein address these limitations by developing tensor-based piezoresistivity constitutive relations. The supposition of this approach is that resistivity changes due to small deformations can be treated as isotropic and be completely described by only two piezoresistive constants — one associated with volumetric strains and a second associated with shear strains. These piezoresistive constants can easily be discerned from simple experiments not unlike the process of determining elastic constants. We demonstrate the potential of this approach by deriving these piezoresistive constants for an experimentally-validated analytical model in the existing literature. This work can enable much more accurate and easily-obtained piezoresistive relations thereby greatly facilitating the potential of resistivity change-based SHM.