Abstract
<title>Abstract</title> <p>The computational cost of multiscale finite element modelling combined with Monte Carlo simulations presents a major challenge for probabilistic material modelling and design of Carbon-Nanotube-Reinforced Polymer Composites (CNTRPCs). While these materials offer outstanding stiffness-to-weight ratios and multifunctional properties, their effective performance is strongly influenced by nanoscale uncertainties such as vacancy defects in Single-Walled Carbon Nanotubes (SWCNTs) and imperfect interfacial bonding. Traditional stochastic analysis requires thousands of finite element simulations to adequately capture the variability in elastic modulus and strength, which is prohibitively expensive for large-scale material design process. To address this limitation, the present work introduces a machine-learning-based modeling framework that significantly accelerates multiscale finite element analysis. Datasets are generated using a Representative Volume Element (RVE) of a CNTRPC, that incorporates a Polyphenylsulfone (PPSU) matrix modeled with Mooney-Rivlin strain energy, an imperfect (16,0) SWCNT modeled with the Morse potential, and a defective interface represented by van der Waals interactions. Monte Carlo simulations introduce stochasticity through atomic vacancies (5% and 10%) at two SWCNT volume fractions (2.5% and 5.0%), generating 10,000 simulations per case of Young’ modulus and yield strength data extracted from finite element tensile analyses. The surrogate approach employs a two-layer feedforward Artificial Neural Network (ANN) trained using the Levenberg-Marquardt backpropagation algorithm. This ANN is used as a non-parametric tool for learning the probability and cumulative distribution function of the simulated mechanical property datasets. Mean square error and regression coefficient are used as performance metrics, benchmarked against Weibull and Gaussian parametric distributions. The NN established is shown to outperform significantly the Weibull distribution as well as the Gaussian distribution. All simulated distributions are left-skewed, confirming the non-Gaussian nature of vacancy-driven mechanical variability and the necessity of non-parametric ANN-based characterization for reliable probabilistic nanocomposite design.</p>