The effective or homogenized properties of particle-reinforced composites, which characterize their macroscopic behavior, do not contain any information about location of individual particles, thus limiting the possibilities of studying the influence of specific distributions of particles on the composites behavior. As a consequence, determination of optimal (in an appropriate sense) configuration of reinforcing particles is also restricted. This problem is addressed in this paper by deriving a mesoscopic model for particle-reinforced composites from the microscopic model of a continuum reinforced by a set of spherical inclusions. As a result, at the mesoscale, the composite is represented as a continuum with point inhomogeneities. At this, characteristics and location of each individual particle enter into the material properties of the composite explicitly. Theoretical derivations are supported by a numerical example of a Mindlin–Reissner thick plate reinforced over its mid-plane by a set of inclusions and subjected to a vertical load distributed over its upper surface.

中文翻译：

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颗粒增强复合材料的介观模型

颗粒增强复合材料的有效或均质特性（表征其宏观行为）不包含有关单个颗粒位置的任何信息，因此限制了研究颗粒特定分布对复合材料性能影响的可能性。结果，也限制了增强颗粒的最佳（在适当的意义上）构型的确定。通过从一组球状夹杂物增强的连续体的微观模型中导出颗粒增强复合材料的介观模型，可以解决此问题。结果，在中尺度上，复合材料表示为具有点不均匀性的连续体。在这，每个颗粒的特性和位置都明确地进入了复合材料的材料特性。Mindlin-Reissner厚板的数值示例通过一组夹杂物加固了中平面，并承受了分布在其上表面的垂直载荷，这为理论推导提供了支持。