# Microstructure-Based Prediction of the Elastic Behaviour of Hydrating Cement Pastes
## 7 Summary and Conclusions  
The present study investigated the evolution of the elastic properties of cement pastes, by performing a continuum micromechanics approach. The cement paste microstructure was simulated using the HYMOSTRUC3D hydration model on a cubic Representative Elementary Volume (REV) with periodic boundary conditions. The obtained REV microstructure was then discretised by using equal small cubic voxels, each one representing a single material phase. A lattice model built from truncated octahedrons was used to predict the elastic properties of the REV microstructure. A specific calibration of the bonds with lattice beams of circular cross-section was used to illustrate the ability of an improved lattice model to represent elastic properties accurately, particularly the Poisson's ratio. The strength of the lattice model to predict the elastic properties of a cement paste was first evaluated using the FEM modelling approach as a reference for comparison. The FEM model was constructed by converting cubic voxels to classical 8-nodded solid hexahedral FEs. The elastic results from the two approaches matched reasonably well. Deviations of the lattice model predictions were further reduced when the elastic properties of lattice beam interfaces were based on the classical Hashin-Shrittkman bounds theory, rather than on the serial/parallel theory. The effective Young's modulus of cement pastes predicted by the lattice and FEM models were then compared with the experimental measurements assessed during hydration by the EMM-ARM testing technique. Both numerical models showed good predictive performances for cement pastes with \(w/c\) ratios of 0.32 and 0.40. However, an underestimation of the effective elastic modulus was obtained for \(w/c\) = 0.48 using both numerical models. Based on a parametric study carried in the present study, the following conclusions can also be drawn:  
1. While the volume of cement was kept constant in the cement hydration modelling, a variation of the Particle Size Distribution (PSD) of cement grains resulted in different morphologies in the cement paste microstructure. When the number of particle increases (adopting a finer PSD curve), finer pore networks are formed, leading to a higher number of solid phase contacts in the microstructure. The higher number of solid connections increases the effective Young's modulus of the cement paste. The phenomenon was opposite when a coarser PSD curve was adopted. Figure 16: Effective Young’s modulus of the cement paste in REV: (**a**) influence of the outer C-S-H Young’s modulus; (**b**) influence of the average Young’s modulus of C-S-H when it is assumed as a single-phase product with no division to inner and outer. Therefore, the pore network morphology has a strong influence on the numerical prediction of the effective elastic modulus of the cement paste. 2. The voxel size, directly related to the microstructure discretisation, plays an important role when using numerical models for predicting the elastic modulus of cement pastes. To reduce the artificial solid connections in digitalised microstructures, the size of voxel shall be adequately small. Decreasing the voxel size to about 70% of the minimum size of cement grains seems to be a promising strategy to improve the accuracy of the numerical predictions. 3. At very early ages, by decreasing Young's modulus of C-S-H the numerical models capture the experimental value of the effective Young's modulus of the cement paste. At these early ages, only low dense C-S-H starts to form in the microstructure, and consequently, a division of the C-S-H product into inner and outer phases leads to an overestimation of the effective Young's modulus of the cement paste.