The concept of representative volume element or RVE is invoked to develop an algorithm for numerical homogenization of fluid filled porous solids. RVE based methods decouple analysis of a composite material into analyses at the local and global levels. The local level analysis models the microstructural details to determine effective properties by applying boundary conditions to the RVE and solving the resultant boundary value problem. The composite structure is then replaced by an equivalent homogeneous material having the calculated effective properties. We combine the features of two techniques: one is the definition of a displacement field for the fluid phase to allow for a definition of a continuous displacement field across the microstructure and the other is the $FE^2$ numerical homogenization that couples the macroscale with the RVE scale via gauss points.

翻译：具有代表性的体积元素或RVE的概念被援引来为液体填充的多孔固体进行数字同质化的算法。基于RVE的方法将综合材料的分析与地方和全球层面的分析脱钩。地方一级的分析模型是微观结构细节,通过对RVE适用边界条件和解决由此产生的边界价值问题来确定有效特性。然后,合成结构被具有计算有效特性的等同同材料所取代。我们结合了两种技术的特征:一种是流体阶段的流体流体场定义,以便能够界定整个微结构的连续迁移场,另一种是将宏观尺度与RVE尺度通过Gauss点对齐的数字同质法。