A 1D-finite element framework for analyzing the cyclic bond response of FRP-strengthened concrete elements

Fiber Reinforced Polymer (FRP) materials are widely used as strengthening systems for concrete and masonry structures. Typically applied to the external surfaces of structural elements, they enhance structural strength and, in some cases, ductility by relying on the bond developed between the FRP and the substrate. The bond behavior of FRPs has been extensively investigated through experimental tests and numerical models, with most studies focusing on monotonic bond behavior. However, relatively few experimental and numerical studies address the cyclic bond behavior of FRPs, despite its significant importance in the context of seismic actions. This paper is part of a research activity carried out by the Authors, aimed at developing numerical approaches that can be easily implemented in commercial computer codes to study the bond behavior of FRP applied to structural substrates. In particular, as a continuation of this research, the 1D-spring modeling approach, widely used for studying monotonic bond behavior, is here specifically enhanced to capture cyclic bond behavior. The model's main features include the use of a tri-linear bond-slip law, commonly adopted in the literature, combined with simple rules to simulate unloading and reloading paths based on interface slip and damage. The proposed model, implemented in Matlab, is validated against experimental results. The results confirm that the model can reproduce the cyclic behavior of FRP-strengthened concrete elements well, including the loss of stiffness and the residual displacements after repeated loading, by using only parameters taken from monotonic tests. The model predicts the maximum bond strength with an error of less than 10 %, and the slope of unloading-reloading branches with differences between 10 % and 18 % for bond lengths from 100 mm to 400 mm, and about 25 % for shorter bond lengths.