Using the finite element code to compute elastic moduli involves some assumptions, some of which are operative at all material ages, and some of which are only important for early-age materials. The first general assumption that is operative at any material age is that cement paste is a linear elastic material, since the code is purely linear elastic. To the extent that cement paste is not a linear elastic material, the code will not accurately predict elastic properties. However, experiment does seem to show that cement paste is generally a linear elastic material , at least for short durations of loading. Second, it is quite possible that the elastic moduli of the C-S-H phase changes with time as the mutual proportion of low density and high density C-S-H changes [5, 6]. This is not taken into account in the model results − the same elastic moduli for C-S-H are taken for all material ages. This could be easily changed, but there is insufficient good data at present to justify such a change. Third, the CEMHYD3D microstructure is not a perfect representation of true cement paste microstructure. The smallest capillary pore size, for example, is no smaller than the voxel size. Critical capillary pores at later material ages that control fluid flow are known to be at the 0.1 µm or smaller size . So, for example, fluid permeability computations will be much too high, roughly by the square of the ratio of voxel size to the critical cement paste pore diameter . But elastic moduli are much more controlled by the solid frame, not the pores, so accurate elastic moduli should be able to be computed, as has been seen in this paper.
At early material ages, the viscoelastic nature of cement paste probably should not be ignored, especially at degrees of hydration smaller than the ones we are using. It is true that the resonant frequency method early age experimental results also ignored the viscoelastic nature of the cement paste at early ages. However, this would tend to make the measured elastic moduli frequency-dependent and higher than they really are , not lower. At early material ages, when the solid frame is much more tenuous, it is clear that a higher resolution (less length per voxel) should be used. Low resolution in the model can mean that particles of different phases can be touching at a corner or edge and be elastically connected, even though, with higher resolution, these particles would become physically disconnected. There are also probably more important effects like those illustrated in Figs. 8 and 10. Digital resolution scaling [16-20] has been studied for other models, and needs to be better studied in the CEMHYD3D model for elastic properties. The results in this paper related to digital resolution at early material ages are preliminary only. A more complete study of early-age phenomena should include methods to more accurately model the kinetics of hydration at early ages − the dissolution bias mentioned earlier  is an incomplete example of what needs to be done. But for now, accurate predictions of cement paste moduli are limited to degrees of hydration above about 50 % hydration, for w/c > 0.45, and above a lower degree of hydration for accurate results at lower w/c ratios. It is possible that insight could be gained into the topology of early-age hydrated structures using the Visual Cement Database .
Finally, an advantage of this approach of combining CEMHYD3D microstructures with finite element solvers is that detailed stress-strain information is available for each phase. A two-phase composite, exact dilute limit result for the coefficient of the phase volume fraction (eq. (6)) was shown to approximately hold true in the multi-phase, concentrated case. This was an unexpected result, and probably holds true generally for any reasonable multi-phase composite, not just cement paste.
No one questions that the cement paste microstructure is complicated. Seeing how each phase, for different w/c ratios and degrees of hydration, contributes to the overall elastic response, should give new insight into experimental results and help clarify the microstructure-elastic property relationships of cement paste, which is one of the fundamental goals of materials science.