Prediction of multi-physical properties of fibre-reinforced composites using deep learning

Abstract

This work develops a convolutional neural network (CNN) based surrogate model for simultaneous multi-physical property prediction from the binary images of fibre-reinforced composites representative volume elements (RVEs). The developed model has direct applications in the inverse design of uni-directional composite materials' microstructures. In the first part of the work, computationally efficient methods and tools are developed to generate a large number of RVEs and their effective properties for a wide range of fibre volume fractions. An overlap-detection approach for arbitrary geometries is developed, which has enabled RVE generation with either circular/non-circular cross section fibres or particles of spherical/non-spherical geometry. Optimisation-based approach, with explicit gradient evaluation, has led to a computationally-efficient RVE generation. The randomness of inclusions in the generated RVEs is assessed using statistical and micro-mechanical methods. Next, a computationally-efficient homogenisation tool is developed, utilising a Variational Asymptotic Method based approach, in Julia. The influence of the fibre cross-sectional profile on the effective multi-physical (thermo-elastic, thermal conduction and piezo-electric) properties is studied using three-dimensional RVEs. For this purpose, five different non-circular fibre cross-sectional profiles (ellipse, rectangle, n-sided regular polygon, n-lobe shape and C-shape) are considered, with equal area. The shape factor, a non-dimensional parameter defined as the ratio of the cross-sectional perimeter to that of a circle of equivalent area, is used to understand the influence of increased cross-sectional perimeter on the effective multi-physical properties across all the considered profiles. It is observed that the influence of the matrix increases initially for about a short range of shape factor, and then the influence of fibre increases monotonically with shape factor. In the second part of the work, a convolutional neural network (CNN) model is developed that takes the binary image of the RVE and constituent material properties as input and then predicts the effective transverse elastic, thermal expansion and thermal conduction properties simultaneously. The training data set, hence the model, is designed for an end-to-end practical range of fibre volume fractions (25–75) and a wide range of material systems, with fibre-matrix property contrast ratios between 2 and 200. A simple constituent material property encoding method is developed so that the model learns to account for material information along with structure information while making predictions. In addition to the unseen samples of the training data domain, the trained model's performance is assessed in the extrapolated range of fibre volume fractions (10 to 25) and property contrasts (200 to 300). It is observed that a significant number of model predictions in the extrapolated domains lie outside the physics-based Hashin-Shtrikman bounds. The Hashin-Shtrikman bounds are used in model training to ensure that the model predictions are always within these bounds.