Multi-scale prediction of chemo-mechanical properties of concrete materials through asymptotic homogenization

In the present contribution, the effective mechanical, diffusive, and chemo-expansive properties of concrete are computed from a multi-scale and multi-physics approach. The distinctive features of the approach are that i) the mechanical and diffusive responses are modelled in a coupled fashion (instead of separately, as is usually done), and that ii) the multi-scale model considers three different scales of observation, which allows for including heterogeneous effects from both the micro- and meso-scales in the effective macro-scale properties of concrete. At the macro-scale, the concrete material is considered as homogeneous, whereas at the meso-scale it consists of particle aggregates embedded in a porous cement paste. At the micro-scale the porous cement paste is described as a two-phase material, composed of a solid cement phase and saturated capillary pores. Adopting a two-level asymptotic homogenization procedure, the effective meso-scale properties of the porous cement paste are computed first, using a unit cell that includes the cement paste and pore characteristics. Subsequently, the obtained meso-scale response of the porous cement paste, together with the aggregate characteristics, defines the material properties of a second unit cell, which is used for calculating the effective macro-scale response of concrete. The distributions of the pores and the aggregates within the unit cells are determined from a uniform, random distribution of points, and their radii are defined from a probability distribution function. The efficacy of the proposed framework is illustrated by studying the effective mesoscopic response of a porous cement paste, which demonstrates the influence of the micro-scale porosity and pore percolation. Next, the effective macroscopic response of concrete is analysed, by considering the influence of the aggregate volume fraction, the mismatches in elastic stiffnesses and diffusivity between the aggregate and the cement paste, and the porosity. The computed effective properties are compared with experimental data from the literature, showing a good agreement.