This paper deals with providing the effective elastic response of three-phase composites consist of a matrix filled with a random suspension of liquid-filled capsules firmly bonded to the matrix in the realm of small deformation theory. The capsules shell (interphases) and the matrix are considered to be elastic solids and the liquid is considered ideal. For this purpose, the solution for dilute concentrations of the interphases and the liquid particles are derived analytically. Then, the dilute solution is passed to an iterative technique to generate the non-dilute version of the solution. The non-dilute response is available in terms of a system of two nonlinear-coupled-ODE-initial-value problems. The results are confronted with the results of a 3D full-field FE analysis and experimental data and a good agreement is observed. The solution, provided here for polydisperse microstructures, allows for considering different thicknesses for the interphases and in turn can possibly account for different physical phenomena like the size and the surface tension effects. A comprehensive study on the effects of interphases (capsules shell) thickness and mechanical properties as well as the volume concentration of the capsules and the liquid particles on the overall elastic properties of three-phase liquid-filled composites are carried out. We show that although the addition of liquid particles to the matrix has deteriorating effects on the overall elastic properties of the composites, proper selection of the interphases can compensate for these negative effects.

本文致力于在小变形理论领域提供三相复合材料的有效弹性响应，该三相复合材料由填充有随机悬浮液的液体填充胶囊组成，该胶囊牢固地粘合在基体上。胶囊壳（相间）和基质被认为是弹性固体，液体被认为是理想的。为此，通过分析得出界面和液体颗粒的稀浓度溶液。然后，将稀释溶液传递给迭代技术以生成溶液的非稀释版本。非稀释响应可用于两个非线性耦合 ODE 初值问题的系统。将结果与3D全场有限元分析结果和实验数据进行比较，观察到良好的一致性。这里为多分散微观结构提供的解决方案允许考虑不同的界面厚度，进而可能解释不同的物理现象，例如尺寸和表面张力效应。综合研究了界面（胶囊壳）厚度和力学性能以及胶囊和液体颗粒的体积浓度对三相液体填充复合材料整体弹性性能的影响。我们表明，尽管向基体中添加液体颗粒会对复合材料的整体弹性性能产生恶化影响，但适当选择界面可以弥补这些负面影响。