Multiscale modelling of transport phenomena for materials with n-layered embedded fibres. Part II : Investigation of fibre packing effects

Abstract : The case of molecular diffusion is investigated and a method is proposed to predict the effective diffusion properties of transversely isotropic composite materials. This paper is the second one of a set of two consecutive papers published in this volume. The general modelling strategy was devised in the first paper (Hervé-Luanco and Joannès, 2016) and applied to the biphasic case in this one. Closed-form analytical expressions are given to investigate fibre packing effects on the effective transverse diffusivity of any unidirectional composite. The specific case of insulated fibres embedded in a diffusive matrix is studied and a clear procedure is then described to determine the model parameters. It is worth noting that only a very simple cross-section image analysis of the unidirectional composite medium is required to provide the two morphological parameters needed to predict the overall diffusivity tensor. Finally, an application on a real microstructure is provided to demonstrate the efficiency of the suggested turnkey method. Very simple analytical calculations make possible parametric studies less expensive than numerical or experimental characterizations.