Multiscale modelling of uniaxial compressive stress-strain behaviour of concrete using analytical homogenisation and damage mechanics

Heterogeneities in concrete manifest at various scales, from aggregates and its interfacial transition zone (ITZ) at macroscale to various hydration products at the microscale. On the application of load, cracks initiate from ITZ and propagate to the bulk cement paste (BCP), leading to the nonlinear stress-strain behaviour of concrete. This paper proposes a novel multiscale analytical approach to simulate the uniaxial stress-strain behaviour of concrete. Initially, the heterogeneous microstructure of ITZ and BCP is simulated using a cement hydration microstructure model (μic). Considering the gradient of phases in ITZ, aggregate gradation and aggregate volume fraction, stresses in the different phases in the ITZ and BCP are calculated by step-wise stress downscaling using continuum micromechanics. The initiation and propagation of cracks in the ITZ and BCP are modelled using damage mechanics. The efficacy of the current analytical approach is validated by comparing with the experimentally observed stress-strain curve. The current model investigates the relation between the macroscopic strain increment with the distribution of strain and the progression of damage in different ITZ layers. Through a parametric study, the influence of w/c ratio (0.30–0.50), aggregate volume fraction (30% and 50%), and aggregate size distribution on the stress-strain behaviour of concrete are discussed.