Prediction of modulus of elasticity based on micromechanics theory and application to low-strength mortars

•A model is developed: the decomposition of a mortar or concrete mesostructure in various volume elements.•Each volume element is made of spherical inclusions in a matrix.•We show the generalized resolution for Mori–Tanaka and self-consistent estimates.•We compare the modeling results with experimental results of low-strength mortars.•Both models perform well when fitted; the input data needed for fitting seems more realistic for the self-consistent estimate than the Mori–Tanaka estimate. The purpose of this article is to present a micro-mechanical modeling approach for multiphase materials made of various inclusions and a matrix. This method is generalized to a composite made of a matrix in which are embedded various inclusions of different radii and properties. The grain size distribution of each type of inclusion is divided into 1 000 elements which volume fractions are determined by linear interpolation. The following input data needs to be known: the elastic properties, the volume fractions of each phase, and the grain size distribution of each aggregate type. The effective properties of the composite are obtained thanks to a loop-type computation of the analytical models described in this article. The generalized method is presented for both Mori–Tanaka and self-consistent estimates. A direct application of this modeling approach to cementitious composites is presented. For the Mori–Tanaka estimate, the aggregates are surrounded by a layer of interfacial transition zone (ITZ) and a layer of cement paste, while air bubbles are considered as mono-sized inclusions with no elastic behavior. For the self-consistent estimate, the cement paste and the air bubbles are both considered as additional single-dimensioned spherical inclusions. A comparison between the experimental and predicted moduli of elasticity is made for typical sand, expanded clay and rubberized mortars with varying volume fractions of aggregates. The predictions show a good agreement with the experimental results for all of the three mortars.