Despite all the progress achieved in the characterization of heterogeneous materials by using multiscale paradigms based on the Representative Volume Element concept (RVE), there are still many aspects that demand ongoing development. We mention, for instance, in-homogeneous media with internal micro-structure comprising a mixture of components that require a dissimilar number/character of primary fields to describe their physical behavior. Micro-structures constituted by a saturated porous matrix (described through the pair displacement/pore pressure fields) endowed with impermeable non-porous solid inclusions (described only by the displacement field) are a typical example among many other practical applications. This new level of heterogeneity, between the set of primal descriptors for each micro-scale constituent, claims detailed revisions and novel adjustments in multiscale RVE-based theories.

中文翻译：

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由饱和多孔基体和固体夹杂物组成的材料的多尺度配方


尽管通过使用基于代表性体积元概念（RVE）的多尺度范式在异质材料表征方面取得了所有进展，但仍有许多方面需要持续开发。例如，我们提到具有内部微观结构的非均质介质，其中包含需要不同数量/特征的主场来描述其物理行为的成分混合物。由饱和多孔基体（通过位移/孔隙压力场对描述）构成的微结构，赋予不渗透的无孔固体包裹体（仅由位移场描述），是许多其他实际应用中的典型例子。每个微观成分的原始描述符集之间的这种新的异质性水平要求对基于 RVE 的多尺度理论进行详细的修订和新颖的调整。