Micromechanical model for the diffusion properties of materials embedding complex structures

Abstract

This paper addresses the issue of the effective diffusion properties of materials with complex microstructure. By using the micromechanical tools, we present a finite element based model suitable for arbitrary shaped and composite inclusion problem in the framework of diffusion properties. A new reformulation of the Eshelby problem (Eshelby, 1957) in diffusion aiming at saving calculation time is presented, solved and results compared to that of the classical approach consisting in imposing the Hashin-type boundary condition at the external boundary of the mesh. Furthermore, the established model is used to compute the second order concentration tensors resulting from the finite element resolution of complex and composite inclusion problem in diffusion for different configurations. The impact of parameters such as the properties and distributions of phases (in the composite inclusion) on the effective properties of the materials are also studied and the results discussed. Finally, the concept of equivalent inclusion is investigated in the present work and proposed as an alternative way to handle complex inclusions problem under some specific conditions. The present work is also suitable for thermal or electrical conduction problems in composite materials since these problems correspond to mathematically equivalent elliptic ones.