An inverse application of unit cells for extracting fibre properties from effective properties of composites

Abstract

A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites for their effective properties. This process is considered as the forward problem and its inverse counterpart is also established in this paper to extract fibre properties from effective properties of composites. It is formulated into a mathematical optimisation problem in which the difference between predicted and provided effective properties is employed as the objective function with the fibre properties as the optimisation variables. The attempt of such an inverse problem is to address the lack of fibre properties for many types of composites commonly in use. The novelty of the paper lies in both sides of the analyses, forward and inverse, as none is available in the literature in the forms as presented in this paper and, more importantly, in the objective of this paper as an attempt to address the pressing and yet long-standing issue of lack of fibre properties. As a verification of the forward analysis, the predicted effective properties of a composite match perfectly with the finite element method (FEM) results. The same case is also employed to verify the inverse analysis by turning the prediction the other way round. Both the forward and inverse analyses have been validated against a series of experimental data. While the forward analysis is generally applicable to any input data as the properties of the constituents, the inverse analysis is sensitive to the input data. Potentially, the inverse analysis would offer a much-needed and also effective tool for the characterisation of fibres. However, reasonable predictions of fibre properties can only be obtained if input data are reasonably consistent.