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.

在许多工程应用中，例如热涂层和结构绝热，二维建模被认为足以识别设计参数。为了有效地评估非均质复合材料的导热系数，本研究开发了二维计算均质化程序。夹杂物在平面内随机分布。引入均质化程序测试的边界条件包括周期性温度，均匀温度和均匀通量边界条件。夹杂物和周围基体之间的结合被认为是不完善的，从而允许在界面处部分传热。通过使用XFEM，可以引入随机分布的包含物，而无需更改矩阵的基本规则网格，从而提供了一种有效的引入包含物的方法。提供了所提出的基于XFEM的计算均化方案的实现细节。通过与可用分析解决方案进行比较来验证结果。显示了假定边界条件对结果的影响。参数研究表明了界面性能，夹杂物的体积比以及夹杂物的分布对复合材料有效导热率的影响。