Multiscale Modeling of Elastic Modulus across Micro-Meso-Macroscales Based on Grid-Nanoindentation Test for Cementitious Materials

Estimation of multiscale elastic parameters is of significance for precise design of cementitious material performances, which depends on the materials’ mineral compositions and microstructures. Nanoindentation technology coupling with statistical analysis is an advanced method to probe the mechanical properties of mineral phases, which bridges the equivalent performance of block cementitious materials by upscaling and the microstructures of minerals by downscaling. In this study, grid nanoindentations and mercury intrusion porosimetry (MIP) were performed on cement paste samples with typical water/cement ratios to obtain the elastic modulus of microscopic phases and porosity. Then, upscaling calculation of equivalent elastic modulus was carried out by homogenization methods including dilute method, Mori-Tanaka (M-T) method, self-consistent method, and interaction direct derivation (IDD) method. Comparing calculations with macrotests of elastic modulus, the results are in good agreement with experiment results after considering the effects of capillary pores, especially by the self-consistent method and IDD method. Furtherly, regression analysis using the self-consistent method was employed to obtain the intrinsic elastic modulus of calcium silicate hydrate (CSH) monomers and packing density of CSH clusters, which is in agreement with reported simulation results by molecular dynamics. This work established the relationships quantitatively among gene minerals with special nanostructures, microstructures of cement pastes and macroelastic performances of block cement materials by a multiscale calculation framework across micro-meso-macroscales, offering a foundation for further multiscale design of high-performance construction materials in civil engineering.