Behaviour of Strain-hardening Cement-based Composites (SHCC) under monotonic and cyclic tensile loading: Part 2 – Modelling

Following the presentation of experimental work in Part I of this article the present part is dedicated to the derivation of constitutive relations for Strain-hardening Cement-based Composites (SHCC) under monotonic and cyclic tensile loading. These constitutive relationships are developed on the basis of a multi-scale modelling approach which considers the determining physical phenomena observed in experimental investigations. The multi-scale model is based on reproducing the fibre-pullout behaviour under monotonic as well as under cyclic loading by a multi-linear approximation, while statistics are used to describe the variation of results as observed in the experiments. Fibre embedment length and inclination serve as main parameters. These responses are further superimposed in order to describe the stress-crack opening behaviour of each individual crack while being loaded, unloaded, or reloaded. The overall stress–strain relationships for material under tensile loading are then derived by considering an increasing number of serial cracks and the contribution of the uncracked matrix. Particular cracking behaviour is adjusted by varying the model parameters. The modelled tensile behaviour of the material is compared with representative results of uniaxial tensile tests performed on the investigated SHCC, and the results of this comparison are discussed.