Bond assessment between rebars embedded into a parent material using a single-function bond-slip model

•To simulate the bond behaviour between rebars and their parent material, a new single-function bond-slip model is proposed.•The proposed bond-slip model requires the calibration, with the experimental data, of three parameters.•The FDM and the FEM are used to simulate the pull-out tests of steel rebars embedded in concrete.•The bond assessment between Fiber Reinforced Polymers rebars and concrete or timber substrates is also analysed.•The high precision obtained in all studied cases suggests that the bond-slip model can simulate any pull-out test. The pull-out test is usually used to evaluate the local bond behaviour between a rebar such as a ribbed steel rebar or a Fiber Reinforced Polymer (FRP) and a parent material, like concrete or timber. Although some codes recommend using a piecewise bond-slip model for ribbed or round steel rebars embedded in concrete, there is no globally accepted bond-slip model for FRP composites. Consequently, this piecewise bond-slip model is usually adapted for FRP composites embedded in a parent material (substrate). The present work therefore aims to propose a novel single-function bond-slip model that may be calibrated and used to model the pull-out test and the detachment process of an embedded rebar from a parent material. The model requires the calibration of three parameters that may vary according to the type of rebar and its parent material. Since the governing equation of the detachment between the rebar and the parent material during a pull-out test has no known analytical solution, the Finite Difference Method (FDM) was applied to find the interfacial slips throughout the embedded length. The results were compared and validated with the experimental pull-out tests of ribbed steel rebars embedded into a concrete block as well as with the numerical results obtained from the use of the Finite Element Method (FEM). To cover a broader range of materials and show the versatility of the novel bond-slip model, the results were also compared with other experimental data available in the literature. The results showed a very high precision of the new bond-slip model when applied to several pull-out tests especially when ribbed steel rebars-to-concrete and FRP-to-concrete interfaces or FRP-to-timber interfaces were used.