The mechanical properties of cement-based materials are almost always of primary importance in the material application since concrete, by far the largest volume use of these materials, is mainly used as a structural material. The mechanical properties of interest are three-fold: short-term deflection, which is controlled by the elastic properties, long-term deflection, which is controlled by the viscoelastic properties, and failure, which is controlled by the strength. If failure is in compression, then we are concerned with the compressive strength; if in tension, we are concerned with the tensile strength.
In this paper, we will only discuss the elastic properties, and will assume that cement paste is a linear elastic material. For a linear elastic material, mathematically the stress, σij, is related to the strain, εkl, via the elastic modulus tensor, Cijkl : σij = Cijkl ekl. Since we are only considering small strains, small with respect to strains at failure, we can ignore failure. Cement-based materials are much more viscoelastic at early ages than at later ages [1]. At ages of 14 d or older, cement paste is well-approximated as a linear elastic material [1], at least for short loading times.
Theoretically predicting the elastic moduli of concrete is a difficult task. First, at the millimeter scale, concrete is a complex, random composite, because of a high loading of a wide size range of fine and coarse aggregates, with all the theoretical difficulties that involves [2-4]. But the cement paste matrix itself is an even more complex, random composite at the micrometer scale. And of course, the main physical phase of cement paste, the calcium-silicate-hydrate (C-S-H)* phase, is a random complex composite at the nanometer scale. So correctly predicting the elastic moduli of concrete, based on knowledge of individual phases, is a multi-scale problem [5, 6]. In this paper, we focus on computing the elastic moduli of cement paste at the micrometer scale, by taking into account all the microstructure at that scale but treating the C-S-H phase as an elastically homogeneous phase. Theoretical predictions are compared quantitatively with experimental results.