Computational Modeling of Carbon Nanotube-Reinforced Polymer Composites using Machine Learning and Peridynamics

Abstract

In this work, data-driven structure-property relations for Carbon Nanotube (CNT)-polymer composites are established using Machine Learning. The stochastic microstructure of computationally generated CNT-polymer composite statistical volume elements (SVEs) is quantified using two-point correlation functions. The two-point correlation functions are represented in a lower-dimensional subspace via Principal Component Analysis (PCA) to make the correlation functions more tractable for use in Machine Learning algorithms for property prediction. Linear regression and Artificial Neural Network (ANN) models are used to establish structure-property linkages that predict the effective stiffness, electrical conductivity, and piezoresistivity coefficients from the principal scores of the correlation functions. It is found that the linear regression and ANN models predict the effective stiffness accurately, but fail to predict the electrical and electro-mechanical properties with sufficient accuracy. It is inferred that the lower-dimensional principal space representation of the two-point correlation functions captures the CNT volume fraction and CNT orientation distribution, both of which control the effective stiffness of the SVEs. However, this representation fails to adequately capture important features which control the electrical conductivity and piezoresistivity of the SVEs, which include the formation of conductive paths between CNTs and the sensitivity of these paths to perturbations in the positions of CNTs due to applied strain. To address these limitation, the SVEs are statistically characterized using two-point cluster functions and two-point blocking functions that capture information about the connectedness of CNTs. In addition, the auto-correlations, two-point cluster functions, and two-point blocking functions of the binarized conductivity contours associated with the SVEs are constructed to capture the conductivity enhancement of the polymer due to the presence of CNTs. Each of these two-point functions is represented in a lower-dimensional space using Principal Component Analysis (PCA). Structure-property linkages are established using Artificial Neural Networks (ANNs) that predict the conductivity and piezoresistivity of the SVEs using these PC scores as input. It is found that the auto-correlations of the binarized conductivity contours constitute the most predictive feature set for the conductivity and piezoresistivity. Furthermore, the two-point cluster and blocking functions fail to reveal additional predictive information about the properties over their auto-correlation counterparts. Finally, the established reduced-order models are used to assign microstructure-informed material properties to the CNT-reinforced polymer binder a multiscale electro-mechanical simulation of a polymer-bonded energetic (PBE). A non-ordinary state-based peridynamic (NOSB-PD) solver is developed to simulate the response of the PBE. A novel bond-based interface is incorporated into the NOSB-PD framework to model the interactions between the different constituent phases. Furthermore, a kinetic damping relaxation (KDR)-based quasi-static solver is incorporated into NOSB-PD to find configurations corresponding to static equilibrium under applied loads. The quasi-static electro-mechanical response of the PBE is then simulated using the developed PD solver.