Multiscale modelling of transport phenomena for materials with n-layered embedded fibres. Part I: Analytical and numerical-based approaches

Abstract

• The overall diffusivity tensor of a multi-layered fibre-reinforced material is given. • Diffusivity is derived from a Morphological Representative Pattern-based approach. • Closed-form analytical relations are proposed depending on morphological parameters. • Diffusivity effects of interphase areas are investigated. Numerical and analytical modelling approaches are often competing to describe a desired phenomenon. However, there is no reason to look for a single method and complementarities between distinct modelling ways are always profitable. This paper, the first of a set of two consecutive papers published in this volume, provides such a modelling methods reconciliation in the case of transport phenomena acting in transversely isotropic multi-phased materials. Microstructural Finite Element Modelling (FEM) helps supplying the analytical implementation for a better description of interactions between the constituents. As an application example, the case of molecular diffusion within a unidirectional composite medium is investigated without any restriction for considering any other transport mechanism. Based on a rational microstructure description, this study proposes a model able to predict the overall diffusion tensor of the composite and investigates more particularly diffusivity effects of interphase areas and fibre packings. For this purpose, a “ n -phase” Generalized Self-Consistent Scheme (GSCS) coupled with a Morphologically Representative Pattern (MRP) approach has been developed. This first part is focused on the modelling strategy and the concept of “transfer matrices” has been used. This approach is applied in Part II (Joannès and Hervé-Luanco, 2016) to study the influence of fibre packings on the effective behaviour of composite materials made of insulated fibres embedded in a diffusive matrix.