On effective thermal conductivity of heterogeneous material: From periodic unit inclusion cell to large representative volume element

Abstract

The custom design of a composite material requires the knowledge of its effective behavior which depends on several parameters such as the properties of the constituents, their distributions, shapes and sizes. In thermal conductivity, all these parameters have a direct and significant influence on the effective thermal conductivity (ETC) of composites. These parameters act differently on the behavior of the composite according to its use as much as a good conductor by improving its ETC or by reducing it by considering it as an insulator. The main goal of this work is an extensive study of all possible situations of ETC by a numerical homogenization technique based on the Finite Elements Method. For this purpose, the two main categories of composites, namely the periodic composites represented by the unit cell and the random RVE, are considered. For each category of composite, different contrasts, different particles’ volume fractions, aspect ratios, positions, and orientations are studied. In order to ensure the simulation results are effective and representative, two boundary conditions, namely Uniform Temperature Gradient Boundary Conditions (UGT) and Periodic Thermal Boundary Conditions (PBC), were imposed on all considered microstructures. The results of this study constitute a synthesis of the effective thermal conductivities of all the possible situations which can be summarized as follows: On the one hand, the reinforcements shape effect is very important irrespective of the nature of the periodic and random composites and on the other hand, the two types of composites do not have the same behavior as that for the reinforcements with a circular or almost circular shape. This study also emphasizes the situations where the ETC can be estimated analytically and when homogenization is necessary. From a practical point of view, and on the basis of the obtained results, this study made it possible to show clearly in which situation the composite becomes more conducting and in the opposite case when it becomes more insulating.