PSI - Issue 78

Francesco Bianco et al. / Procedia Structural Integrity 78 (2026) 41–48

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Fig. 3. Schematization of the reloading phase of shear springs.

2.2. Validation The proposed modeling approach and the simplified rules introduced for schematizing the cyclic behavior of shear springs have been implemented in MATLAB, improving an earlier interface law and allowing comparison with experimental benchmarks. Because of the nonlinearity introduced by unloading and reloading, a modified Newton based method was adopted to improve convergence. This algorithm includes a damping factor to better handle the cycles and uses a relative error criterion to check for convergence. The validation of the proposed model was carried out using experimental data from the study by Nigro et al. (2011), which included both monotonic and cyclic single-lap shear tests on concrete specimens strengthened with CFRP. A total of 28 tests were performed on concrete prisms (150×200×500 mm) with CFRP sheets applied over different bond lengths: 400 mm, 100 mm, and 50 mm. However, only the first two were considered here. To assess the cyclic response, selected specimens were subjected to four series of ten repeated load-unload cycles, with increasing load levels equal to 15%, 30%, 50%, 70%, and 90% of the maximum force obtained from the monotonic tests. Before running the cyclic simulations, the shear stress–slip relationship at the interface was calibrated using data from the monotonic experiments. An initial tri-linear model was defined based on guidelines from the Italian standard CNR-DT200 (2013). This model was then refined by adjusting parameters such as peak shear strength, initial stiffness, and slip at failure, to improve agreement with experimental curves. The results of the cyclic simulations, shown in the figures for both sheet- and plate-reinforced specimens, confirm that the model effectively captures the mechanical behavior. The imposed displacements for cyclic analyses were taken from the monotonic numerical curves to match the experimental load levels. The model demonstrated a good match with experimental data, especially in terms of residual force and response during the cycles. Although unloading and reloading branches partially overlapped, the slopes of the numerical response closely followed the experimental trends, confirming that the model reliably simulates progressive damage at the interface.