  A finite-element approach based on the first-order FE 2 homogenisation
technique is formulated to analyse the alkali-silica reaction-induced damage in
concrete structures, by linking the concrete degradation at the macro-scale to
the reaction extent at the meso-scale. At the meso-scale level, concrete is
considered as a heterogeneous material consisting of aggregates embedded in a
mortar matrix. The mechanical effects of the Alkali-Silica Reaction (ASR) are
modelled through the application of temperature-dependent eigenstrains in
several localised spots inside the aggregates and the mechanical degradation of
concrete is modelled using continuous damage model, which is capable of
reproducing the complex ASR crack networks. Then, the effective stiffness
tensor and the effective stress tensor for each macroscopic finite element are
computed by homogenising the mechanical response of the corresponding
representative volume element (RVE), thus avoiding the use of phenomenological
constitutive laws at the macro-scale. Convergence between macro- and
meso-scales is achieved via an iterative procedure. A 2D model of an ASR
laboratory specimen is analysed as a proof of concept. The model is able to
account for the loading applied at the macro-scale and the ASR-product
expansion at the meso-scale. The results demonstrate that the macroscopic
stress state influences the orientation of damage inside the underlying RVEs.
The effective stiffness becomes anisotropic in cases where damage is aligned
inside the RVE.
