A comprehensive multiscale model for elucidating strain-dependent piezoresistive behavior of porous MWCNTs/polymer nanocomposites

Carbon-based nanocomposites sensors are well known to possess excellent electrical conductivity and strain sensing capabilities, widely used for structural health monitoring, wearable flexible electronics, and biomedical applications fields. Such sensing capabilities originate from the electromechanical behaviors of sensitive nanocomposites, which can be designed with enhanced piezoresistive performances by constructing microstructures such as porous structures. However, it remains a challenge to establish an efficient homogenized electromechanical model to elucidate the piezoresistive behavior of porous microstructured nanocomposites. Herein, we developed a multiscale homogenization method for piezoresistive behavior of porous MWCNTs/polymer nanocomposites. For the specific three-phase inclusion problem, we consider the influences of pores, MWCNTs agglomerates, and volume fractions of porosities and MWCNTs fillers in nanocomposites to predict effective electrical conductivity affected by the volume fraction of MWCNTs fillers and loadings. We first utilized the Mori-Tanaka method (MTM) considering porosity and dynamic far-field matching approach to obtain equivalent mechanical moduli and effective electrical conductivities, and then leverage strain-dependent tunneling distances to achieve the coupling of mechanical and electrical constitutive relationships. Furthermore, we introduced a spring layer to model the imperfect bonding between carbon-based fillers and polymer matrix, incorporating the impact of interfaces on both elastic and electrical properties of nanocomposites. Consequently, the coupling influences of MWCNTs volume fractions, strain loadings, interface, agglomerates, and porosities on piezoresistive behaviors of porous MWCNTs/polymer nanocomposites were studied in details. Finally, this present theoretical model can offer guidance of customized designing carbon-based microstructured nanocomposites sensory systems.