The Representative Volume Element (RVE) plays a central role in the homogenization of random heterogeneous microstructures, especially for composite and porous materials, with a view to predicting their effective properties. A quantitative evaluation of its size is proposed in this work in linear elasticity and linear thermal conductivity of random heterogeneous materials. A RVE can be associated with different physical and statistical properties of microstructures. The methodology is applied to specific two–phase microstructure–based random sets. Statistical parameters are introduced to study the variation in the RVE size versus volume fractions of components and the contrast in their properties. The key notion of the integral range is introduced to determine these variations. For a given desired precision, we can provide a minimal volume size for the computation of effective mechanical and thermal properties. Numerical simulations are performed to demonstrate that a volume exists which is statistically representative of random microstructures. This finding is an important component for homogenization–based multiscale modeling of materials.

代表性体积元素（RVE）在随机异质微观结构的均质化中起着核心作用，特别是对于复合材料和多孔材料，以预测其有效性能。在这项工作中，提出了一种定量评估其随机异质材料的线性弹性和线性热导率的方法。RVE可以与微结构的不同物理和统计特性相关联。该方法适用于基于特定的两阶段微结构的随机集。引入统计参数来研究RVE大小随组分体积分数的变化及其特性的对比。引入积分范围的关键概念来确定这些变化。对于给定的所需精度，我们可以提供最小的体积来计算有效的机械和热性能。进行数值模拟以证明存在一定体积，该体积在统计学上代表随机微结构。这一发现是基于均质化的材料多尺度建模的重要组成部分。