The prediction of the effective thermal conductivity of composite materials is of paramount importance for many applications. While there exist correlations for bi-phase materials made of rigid spherical inclusions in a continuum matrix, there is lack of correlations for composites whose spherical phase is densely packed, as in densified granular materials or in foams with overlapping bubbles. In this study we combine a packing algorithm with a finite difference solver to determine the effective thermal conductivity when the spherical phase is highly overlapping, with volume fraction larger than 55%, for all the conductivity ratios of the two phases. Three fit relations are proposed to encompass the whole range of conductivities, showing good accuracy for both simulated and experimental data and outperforming existing relations commonly used for the estimation of the effective thermal conductivity. Our relations can also be used for estimating the effective electric conductivity, magnetic permeability and mass diffusivity in continuum regime.

预测复合材料的有效热导率对于许多应用至关重要。虽然在连续基体中由刚性球形夹杂物制成的双相材料存在相关性，但对于球相密集堆积的复合材料，如致密颗粒材料或具有重叠气泡的泡沫，则缺乏相关性。在这项研究中，我们将填充算法与有限差分求解器相结合，以确定当球相高度重叠且体积分数大于 55% 时，对于两相的所有传导率比，有效热导率。提出了三种拟合关系以涵盖整个电导率范围，模拟和实验数据均显示出良好的准确性，并且优于通常用于估计有效热导率的现有关系。我们的关系式还可用于估计连续介质中的有效电导率、磁导率和质量扩散率。