In this review, we discuss replacement (or substitution) relations that quantify changes in various physical properties of heterogeneous materials, produced by variation in the properties of one (or several) of the constituents while keeping the microstructure unmodified. The latter may be formed by interconnected pores, isolated inhomogeneities (cracks, pores, inclusions), or represent the combination of the two. Replacement relations play important role in different branches of applied science, but they are most widely used in geophysics (Gassmann equation), where it is of considerable practical interest to predict how the effective elastic properties of a rock change when the pore-filling material is changed. It allows one to distinguish between, for example, oil and water saturation. Another important application following from the replacement relations is a new methodology to evaluate physical properties (thermal conductivity or elastic moduli) of material particles that cannot be directly measured with reliable accuracy (due to their small size, for example). We overview various approaches to the problem and then advance the most general method based on the concept of property contribution tensors. This method leads to replacement relations that are valid for materials of arbitrary anisotropy and have explicit closed form. We discuss replacement relations for elastic properties and thermal (or electric) conductivity and compare the relations derived by different ways.

在这篇综述中，我们讨论了替换（或替代）关系，该关系量化了异质材料各种物理特性的变化，这些变化是由一种（或几种）成分的特性变化而产生的，同时保持微观结构不变。后者可以由相互连接的孔，孤立的不均匀性（裂缝，孔，夹杂物）形成，或代表两者的组合。置换关系在应用科学的各个分支中都起着重要作用，但它们在地球物理学（Gassmann方程）中得到了最广泛的应用，人们对于预测岩石的有效弹性特性如何改变孔隙填充材料具有很大的实际意义。改变了。它使人们可以区分例如油和水饱和度。替代关系之后的另一个重要应用是评估材料颗粒的物理性质（导热系数或弹性模量）的新方法，这些材料无法以可靠的精度直接测量（例如，由于其尺寸小）。我们概述了解决该问题的各种方法，然后基于属性贡献张量的概念提出了最通用的方法。此方法导致的替换关系对于任意各向异性的材料均有效，并且具有显式的封闭形式。我们讨论了弹性和热（或电）导率的替换关系，并比较了通过不同方式得出的关系。