Statistical variability of mechanical fields in thermo-poro-elasticity: Multiscale analytical estimations applied to cement-based materials at early-age

Analytical homogenization provides information about the average mechanical fields but can also be used to obtain information about the statistical variability or fluctuations of these fields. Here, we present analytical estimations of the fluctuations of elastic stresses within cement-based materials (CBM). Mori-Tanaka, self-consistent and generalized self-consistent schemes are combined to represent the multiscale character of CBM. The second moment of mechanical fields is derived from the internal energy. The presence of transformation fields and resulting fluctuations are considered. We account for the evolution of the volume fractions of phases due to cement hydration. Scenarios considering or not the ITZ are studied. Our estimations are dependent on load and representation CBM microstructure. The obtained standard deviation of stresses in C-S-H are on the order of the stresses applied at concrete scale. We provide estimations of the compressive strength of a cement paste at early-age using our results of fluctuation of stresses.