PSI - Issue 78

Enes Krasniqi et al. / Procedia Structural Integrity 78 (2026) 261–268

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Monitoring points were strategically integrated into the numerical models to capture essential response variables, including displacements, stress distributions, crack opening displacements, and other localized effects. Figure 3 illustrates the location of these virtual sensors. The loading protocol was designed to replicate the experimental procedure and consisted of two main stages, summarized where the first stage involved the application of self-weight and initial support constraints in a single load step. The second stage involved incremental tensile loading applied over 100 load steps, progressively increasing the displacement at the free end of the bar from zero up to and beyond the ultimate load capacity, thereby capturing both pre-peak and post-peak structural behaviour, including softening and failure mechanisms. The loads were applied incrementally, ensuring that each subsequent step accumulated over the prior state, thus providing a robust simulation of the nonlinear response of the anchorage systems. This comprehensive numerical modelling approach allowed for detailed investigation into the structural behaviour of mechanically anchored connections, enabling a robust comparison with experimental observations and providing valuable insights into failure mechanisms and design optimization for precast concrete connections. 4. Material Parameters The finite element simulations in this study incorporated advanced constitutive models to capture the nonlinear behaviour of concrete, reinforcing steel, and their interfaces. This section provides a comprehensive overview of the material parameters used for each component of the numerical models, including concrete modelled with a fracture– plastic constitutive law, steel reinforcement modelled via von Mises plasticity, and the interface between steel and concrete represented through a dedicated contact formulation. Mean strength were considered following standard material testing carried out alongside the pull-out tests. 5.1. Concrete material model The nonlinear behavior of concrete was simulated using the fracture–plastic constitutive model implemented in ATENA Science, which combines smeared crack theory with nonlinear fracture mechanics to represent cracking, crushing, and post-peak degradation. Key parameters include an elastic modulus of 36 GPa and a Poisson’s ratio of 0.20. The compressive strength was set as 53 MPa, while the tensile strength was set at 3.8 MPa. Fracture energy � governing crack propagation was defined as 149 N/m, corresponding to the exponential tension softening law. Compressive crushing initiation occurs at 0.75 times the compressive strength (approximately −8 MPa), with the critical compressive strain �� defined as −3‰ and a plastic strain limit of −0.00135 beyond which localized crushing develops, as illustrated in Figure 4. Crack localization and mesh-objective softening behavior were controlled via the crack band approach, with an aggregate size of 20 mm guiding the characteristic length. Additional parameters include a dilatancy angle (Beta) set to zero and an eccentricity factor of 0.51 to define the shape of the failure surface in three dimensions, reflecting recommendations for high-strength concrete (fib, 2013). A compressive strength reduction factor of 0.8 was applied to account for the effects of transverse cracking. In all simulations, the concrete was considered fully crushed when the absolute value of compressive strain exceeded the threshold ��� =−0.003 , consistent with the limit states defined in Model Code 2010 (fib, 2013) and widely accepted in modern design practices for characterizing concrete’s ultimate compressive behaviour. 5.2 Steel reinforcement model The reinforcing steel, including the threaded bars, was modeled using the von Mises plasticity model with bilinear isotropic hardening behavior. The elastic modulus was set at 210 GPa, with a Poisson’s ratio of 0.30 and a density of 7850 kg/m³. The thermal expansion coefficient was defined as 1.2×10 �� C �� . The steel exhibited a yield strength of 660 MPa, with no hardening slope specified (hardening modulus =0 MPa), indicating a perfectly plastic behavior post-yield. The ultimate strain capacity was assumed to be 10%, ensuring the model could capture significant plastic deformation prior to fracture, consistent with the mechanical properties of high-strength steel bars used in precast applications.