We present an application of data analytics and supervised machine learning to allow accurate predictions of the macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane. Predictions are obtained from the analysis of an image of the material microstructure, as well as knowledge of the constitutive models for fibres and matrix, without performing physically-based calculations. The computational framework is based on evaluating the 2-point correlation function of the images of 1800 microstructures, followed by dimensionality reduction via principal component analysis. Finite element (FE) simulations are performed on 1800 corresponding statistical volume elements (SVEs) representing cylindrical fibres in a continuous matrix, loaded in the transverse plane. A supervised machine learning (ML) exercise is performed, employing a gradient-boosted tree regression model with 10-fold cross-validation strategy. The model obtained is able to accurately predict the homogenized properties of arbitrary microstructures.

A new algorithm to generate random spatial distributions of cylindrical fibres and spheres is developed based on a constrained optimization formulation. All filler particles are generated simultaneously within the specimen domain; subsequently their position is iteratively perturbed to remove particle overlapping. The algorithm is able to achieve volume fractions of up to 0.8 in the case of circular cylindrical fibres of equal diameter; the method can be applied to any statistical distribution of fibre diameters. The spatial distribution of fibres and spheres is analysed by plotting spatial statistical metrics; it is shown that the microstructures generated are spatially random and similar to those observed in real fibre composites. The algorithm is employed to effectively predict the transversely isotropic elastic, damping and plastic properties of a unidirectional fibre composite by analysis of an RVE of smaller size than previously reported.

We perform finite element analysis of the mechanical response of random RVEs representing the microstructure of a unidirectional (UD) fibre composite, predicting its anisotropic stiffness and damping properties and their sensitivity to temperature and frequency, using as inputs only the measured response of the constituents. The simulations are validated by DMTA measurements on a UD composite; then, the numerical predictions are compared to those of previously published theoretical models. New equations are proposed to predict the viscoelastic constants, providing better accuracy than existing models. The accuracy of these new equations is tested, over wide ranges of fibre volume fractions and stiffness ratios of the constituents, against the numerical predictions

Finite Element (FE) simulations are conducted to predict the viscoelastic properties of unidirectional (UD) fibre composites. The response of both periodic unit cells and random stochastic volume elements (SVEs) is analysed; the fibres are assumed to behave as linear elastic isotropic solids while the matrix is taken as a linear viscoelastic solid. Monte Carlo analyses are conducted to determine the probability distributions of all viscoelastic properties.Simulations are conducted on SVEs of increasing size in order to determine the size of a representative volume element (RVE); for the fibre volume fractions analysed (0.3 and 0.6), we conclude that elastic properties can be effectively predicted using RVEs of size equal to 24 times the fibre radius, whereas numerical predictions of loss factors require smaller RVEs, of size equal to 12 times the fibre radius. The predictions of the FE simulations are compared to those of existing theories and it is found that the Mori-Tanaka [1] and Lielens [2] models are the most effective in predicting the anisotropic viscoelastic response of the RVE.