This work reviews state of the art representative volume element (RVE) generation techniques for heterogeneous materials. To this end, we present a systematic classification considering a wide range of heterogeneous materials of engineering interest. Here, we divide heterogeneous solids into porous and non-porous media, with 0<$0<$ void volume fraction <1$<1$ and void volume fraction =0$=0$, respectively. Further subdivisions are realized based on various morphological features. The corresponding generation methods are classified into three categories: (i) experimental methods targeting reconstruction through experimental characterization of the microstructure, (ii) physics based methods targeting simulation of the physical process(es) responsible for the microstructure formation and evolution, and (iii) geometrical methods concentrating solely on mimicking the morphology (ignoring the physical basis of the microstructure formation process). These comprise of various mathematical tools such as digital image correlation, tessellation, random field generation, differential equation solvers, etc. For completeness, relevant up-to-date software tools, used at various stages of RVE generation — either commercial or open-source — are summarized. Considered methods are reviewed based on their efficiency and predictive performance with respect to geometrical and topological properties of the microstructures.

这项工作回顾了异构材料的最先进的代表性体积元素（RVE）生成技术。为此，我们提出了一种系统的分类方法，其中考虑了广泛的具有工程意义的异质材料。在这里，我们将非均质固体分为多孔介质和无孔介质，其中0 <$0<$空隙体积分数<1$<\mathrm{1个}$和空隙体积分数= 0$=0$， 分别。基于各种形态特征，可以实现进一步的细分。相应的生成方法分为三类：（i）通过微观结构的实验表征进行重建的实验方法；（ii）以负责微观结构形成和演化的物理过程的模拟为基础的基于物理的方法；以及（iii） ）仅专注于模仿形态的几何方法（忽略微观结构形成过程的物理基础）。这些工具包括各种数学工具，例如数字图像相关性，细分，细分，随机场生成，微分方程求解器等。为完整起见，请使用相关的最新软件工具，总结了在RVE生成的各个阶段（商业或开源）中使用的方法。根据有关微结构的几何和拓扑特性的效率和预测性能，对考虑的方法进行了回顾。