Quantitative analysis of the representative volume element of polymer grouting materials based on geometric homogenization

Abstract

In recent years, polymer grouting material has been applied to engineering combined with the development of grouting technology. Two-component foaming polyurethane is one type of water insensitive polymer grouting material, in which the cell structure plays a key role on its physical properties. To explore the impact of the microstructure of the polyurethane polymer on its macroscopic performance, it is necessary to study the representative volume element (RVE) quantitatively. In this study, the definition of the geometric RVE for this kind of polymer material is given. Taking the cell content, average cell diameter, and standard deviation as microscopic statistical characteristics of polymer meso-structure, the method to determine quantitatively the RVE of polymer is proposed. Scanning electron microscopy (SEM) images of two-component foaming polyurethane specimens with different densities were observed, and the mesoscopic characteristics were calculated. Random distributed cells were selected to establish the 2D Voronoi polygon models for low-density polymers and the 2D circular models for medium- and high-density polymers, respectively. Considering the random position of the overall numerical sample and the increasing sized sample, the size of the geometric RVE for polymers with different densities were calculated based on each microscopic statistical characteristic, and the influence of the density and microscopic statistical characteristics on the size of the polymer geometric RVE was analyzed. The results show that the RVE size of the polymers with different densities is approximately 15–21 times of the average cell diameter and the main factor of RVE size is cell content.