Novel closure approximation for prediction of the effective elastic properties of composites with discontinuous reinforcement

The paper introduces a novel closure approximation method for the determination of the fourth-order orientation tensor in terms of known second-order tensor. The fourth-order orientation tensor must be known to predict the effective elastic properties of composites with misaligned fibres but very often only the second-order orientation is available. The proposed method operates on a set of outcomes of optimization based on a genetic algorithm. In consequence, it leads to obtaining distributions of effective elastic constants instead of deterministic quantities. Results obtained by using the novel approach have been compared with results based on exact fourth-order orientation tensor, tensor known from experimental data and determined by using popular closure approximations from literature. Furthermore, the obtained results have been compared with results of finite element analysis based on geometrical models representing the microstructure which contains several hundred fibres. The new method provides high accuracy of elastic constant predictions for all studied fibre orientation distributions, which distinguishes it from the closure approximation methods known from the literature. Moreover, results obtained in form of distributions give an insight into the uncertainty of the predictions.