An XFEM-based computational homogenization framework for thermal conductivity evaluation of composites with imperfectly bonded inclusions

Abstract

In many engineering applications, such as thermal coating and structural insulation, 2D modelling is deemed sufficient to identify design parameters. For the effective thermal conductivity evaluation of heterogeneous composites, a 2D computational homogenization procedure is developed in this study. The inclusions are distributed randomly within the plane. The boundary conditions tested for homogenization procedure introduced include the periodic temperature, uniform temperature, and uniform flux boundary conditions. The bond between the inclusions and the surrounding matrix is assumed imperfect allowing partial heat transfer at the interface. Randomly distributed inclusions can be introduced without altering the underlying regular mesh of the matrix by using the XFEM, providing an efficient way of introducing the inclusions. Implementation details of the proposed computational homogenization scheme based on the XFEM are provided. The results are validated by comparisons with available analytical solutions. Effect of assumed boundary conditions on the results are shown. Parametric studies illustrate the influence of the interface properties, volume ratio of inclusions as well as the distributions of the inclusions on the effective thermal conductivity of composites.