Derivation of a multi-scale model for Strain-Hardening Cement-based Composites (SHCC) under monotonic and cyclic tensile loading

Paper presents the derivation of constitutive relations for Strain-Hardening Cementbased Composites (SHCC) under monotonic and cyclic tensile loading. These constitutive relations result from a sound physical model which links different levels of observation from the behaviour of individual fibres to the overall response of the composite material. As an experimental basis for modelling, single fibre pullout tests were used. First, the pullout behaviour as well as de-bonding and failure of single fibre incorporated in the composite are presented and discussed for monotonic tests with regard to different testing parameters. Subsequently, a set of multi-linear descriptions for the fibre-matrix interaction can be defined. Statistical approach is employed in order to deal with the variance of results observed. The stress-displacement relation for one representative crack in SHCC is obtained by adding crack-bridging contributions of all fibres crossing the crack plane. Fibre distribution in the composite as well as the embedded lengths and inclinations of fibres involved in crack bridging are the main parameters considered. Furthermore, the behaviour of single fibre pullout under cyclic loading is investigated. The results obtained are incorporated into the model, so that also unloading and reloading stress-crack opening relations for a single crack in SHCC are derived. Based on these formulas constitutive relations for macrostress- strain behaviour of SHCC (considering multiple cracking) will be developed in the next step.