A Simplified Analytical Model for FRP-Strengthened Curved Brittle Substrates Using the Multi-Linear Bond-Slip Law

The utilization of fiber-reinforced polymer (FRP) composites for building reinforcement has gained widespread acceptance. However, the bond behavior between externally applied composites and strengthened substrates, which are crucial for system efficacy, has primarily focused on flat surfaces. Yet, the challenge of curved substrates, common in masonry arches and vaults, remains less explored. This study introduces a classical analytical model addressing the bond behavior between FRP plates and curved substrates. This classical approach is structured upon a simplified model that concentrates all the non-linearities of the FRP–substrate interface. The interface is described through a universal multi-linear stress–slip relationship, with the influence of the curved substrate being considered by the normal stress that impacts the interface law. Closed-form solutions for distinct bond-slip law stages are derived and verified against the previous study. Through comparisons with existing experimental data and simulations, this approach is able to predict the maximum load, the trends of the global load-slip curves, and give insights into detailed local behavior. Additionally, the exploration of employing neural networks for determining the interface law exhibits promising outcomes