An analytical model based on strain localisation for the study of size-scale and slenderness effects in uniaxial compression tests

In this paper, an analytical model based on the concept of strain localisation is proposed for the analysis and prediction of the response of quasi-brittle materials in uniaxial compression tests, such as mortar, plain concrete with different compression strengths, as well as fibre-reinforced concrete. The proposed approach, referred to as Overlapping Crack Model, relies only on a pair of material constitutive laws, in close analogy with the Cohesive Crack Model: a stress-strain relationship describing the pre-peak behaviour of the material and a stress-interpenetration relationship for the description of the post-peak response. In the paper it will be shown how the stress-interpenetration relationship can be deduced from experimental data and how it depends on the compression strength and on the crushing energy of the tested materials. A wide comparison between the stress-displacement curves predicted by the proposed model and those experimentally found in the literature will show the effectiveness of the present approach to capture both stable softening or sharp snap-back post-peak branches by varying the slenderness or the size-scale of the tested samples.