Graphene nanoplatelet (GNP)-reinforced epoxy nanocomposites have attracted significant attention due to their potential for enhanced electrical conductivity at low filler loadings, offering multifunctional properties for a wide range of applications. However, accurately predicting electrical percolation remains challenging due to the complex interplay between filler distribution and interparticle interactions. Only a few micromechanical models have been developed, where 2D GNP flakes are typically placed in a 3D representative volume element (RVE) without overlapping. Since they cannot share any nodes and the matrix is extremely insulating, the electrical connection between adjacent, non-touching flakes is then modeled using a tunneling conductance function, such as the one proposed by Lu et al. (2017) [1].
This work aims to develop a finite element (FE)-based micromechanical model capable of simulating the electrical conductivity and percolation behavior of GNP-filled epoxy nanocomposites using an alternative approach. Instead of a tunneling function, the electrical contact between flakes closer than a given cutoff distance is modeled as a conductive surface with a constant resistivity. This prevents the non-physical overlap of flakes while allowing direct control over the resistance between platelets.
For that, 3D representative volume elements (RVE) are generated, containing randomly distributed, non-overlapping GNP flakes modeled as two-dimensional disks embedded in an insulating epoxy matrix. Electrical connectivity between neighboring flakes was represented as conductive surfaces introduced when interparticle distance fell below a prescribed cutoff. A custom MATLAB algorithm was developed to generate flake geometry, orientation, and spatial distribution while enforcing periodic boundary conditions. The governing electrostatic problem was formulated on the surfaces of the conductive domains and solved using computational homogenization in a FE framework using COMSOL Multiphysics. Model parameters, including contact cutoff distance, contact resistivity, and RVE size, were calibrated against experimental data.
The model successfully reproduced the experimentally observed electrical percolation threshold at 0.5 wt.% GNP loading with a critical cutoff distance of approximately 0.45 µm, consistent with physical considerations based on van der Waals interactions. The contact resistance between flakes was found to be a dominant factor governing the composite conductivity, with optimal agreement obtained for a normalized contact conductivity of 10-3 relative to the intrinsic GNP conductivity. Additionally, an RVE size of 10 µm was determined to ensure convergence of the homogenized electrical response. The model captured the transition from insulating to conductive behavior as filler content increased, reproducing both the percolation threshold and the saturation of conductivity at higher loadings.
The proposed FE-based modeling framework provides a simple and computationally efficient approach for modeling electrical conductivity in GNP-reinforced nanocomposites. By replacing tunneling formulations with conductive contact surfaces, the model offers improved physical interpretability and ease of implementation. The results highlight the critical role of interparticle contact resistance and demonstrate the capability of the approach to capture percolation behavior in agreement with experimental observations. This framework can be extended to other conductive nanocomposite systems and serves as a valuable tool for microstructure-informed material design.
[1] Lu et al. Journal of Computational Physics, v. 337 116-131 (2017)
Comissão Organizadora
Pedro Alves da Silva Autreto
Comissão Científica
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