The objective of this work is inclusion of the Steigmann-Ogden interface in the Method of Conditional Moments to investigate the influence of surface effects on the effective properties of random particulate composites. The particular focus is centered on accounting for the surface bending stiffness. To this end, the notion of the energy-equivalent inhomogeneity developed for Gurtin–Murdoch interface is generalized to include the surface bending contribution. The crucial aspect of that generalization is identification of the formula defining energy associated with the surface bending. With the help of that formula, the real nano-particle and its surface are replaced by equivalent inhomogeneity with properties incorporating the surface effects. Closed-form expressions for the effective moduli of a composite with a matrix and randomly distributed spherical inhomogeneities are derived. The normalized shear moduli of nanoporous material as a function of void volume fraction is analyzed and evaluated in the context of other theoretical predictions.

这项工作的目的是在条件矩方法中包括Steigmann-Ogden界面，以研究表面效应对无规颗粒复合材料有效性能的影响。特别关注的重点是考虑表面弯曲刚度。为此，为Gurtin-Murdoch界面开发的能量等效不均匀性的概念被概括为包括表面弯曲贡献。该概括的关键方面是确定定义与表面弯曲相关的能量的公式。借助该公式，真正的纳米粒子及其表面被等效的不均匀性所取代，具有包含表面效果的特性。推导了具有矩阵和随机分布的球形不均匀性的复合材料有效模块的闭式表达式。纳米多孔材料的归一化剪切模量作为空隙体积分数的函数，在其他理论预测的背景下进行了分析和评估。