It is well-known by now that the Hashin–Shtrikman bounds imply that the two-point correlation functions are not in general sufficient to estimate accurately the response of composites, especially when their underlying phases exhibit infinite contrast, e.g., porous materials. Starting from this longstanding, albeit qualitative result, this work investigates quantitatively the relevance of using two-point correlations to model the effective elastic properties of specific isotropic porous materials with and without connectivity. To achieve this in an unambiguous manner, we propose three different microstructures that share almost identical two-point statistics by design but are rather different morphologically. The choice of these microstructures is driven by their wide use in several practical problems ranging from polymers to geomaterials. The first microstructure is obtained by a random sequential adsorption (RSA) of non-overlapping, polydisperse, spherical and ellipsoidal voids oriented randomly in a unit-cell. The second one, termed connected random sequential adsorption (CRSA), is obtained from the first one by adding controlled connectivity via cylindrical channels of circular cross-section. The porosity resulting from connectivity is compensated by reducing the size of the existing voids to have the same overall porosity. Interestingly, we find that connectivity does not affect the corresponding two-point statistics. Finally, using as an input the numerical one- and two-point correlations of the RSA, we reconstruct a thresholded Gaussian random field (TGRF) microstructure. Using FFT numerical simulations, we show that the resulting effective elastic properties are very different for the three generated microstructures, despite them sharing nearly the same two-point correlation functions. We show, further, that the introduction of connectivity, and in particular the partial volume fraction of the connected channels, even small, affects strongly the resulting effective elasticity of the composite.

众所周知，Hashin-Shtrikman 界限意味着两点相关函数通常不足以准确估计复合材料的响应，尤其是当它们的底层相表现出无限对比度时，例如多孔材料。从这个长期存在的定性结果开始，这项工作定量研究了使用两点相关性来模拟具有和不具有连通性的特定各向同性多孔材料的有效弹性特性的相关性。为了以明确的方式实现这一点，我们提出了三种不同的微观结构，它们在设计上共享几乎相同的两点统计数据，但在形态上却大不相同。这些微结构的选择是由于它们在从聚合物到地质材料的几个实际问题中的广泛应用。第一个微结构是通过随机顺序吸附 (RSA) 在晶胞中随机取向的非重叠、多分散、球形和椭圆形空隙获得的。第二个称为连接随机顺序吸附 (CRSA)，它是通过通过圆形横截面的圆柱形通道添加受控连接从第一个获得的。通过减小现有空隙的尺寸以具有相同的总体孔隙率来补偿由连通性产生的孔隙率。有趣的是，我们发现连通性不影响相应的两点统计。最后，使用 RSA 的数值单点和两点相关性作为输入，我们重建阈值高斯随机场 (TGRF) 微观结构。使用FFT数值模拟，我们表明，尽管它们共享几乎相同的两点相关函数，但产生的三种微结构的有效弹性性能却大不相同。我们进一步表明，连接性的引入，特别是连接通道的部分体积分数，即使很小，也会强烈影响复合材料的有效弹性。