PSI - Issue 78

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

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Figure 4. Stress–strain diagram for concrete showing parameters �� and �� .

5.3 Interface material model The interface between the steel threaded bar and the surrounding grout or concrete was modeled using a dedicated contact formulation based on a Mohr–Coulomb criterion with tension cut-off, ensuring accurate simulation of bond– slip and possible debonding phenomena. Normal and tangential stiffnesses were both set to 5×10 � MN/m, ensuring high initial stiffness to resist relative movement. Cohesion was modeled as 0.01 MPa, with a friction coefficient of 0.4 to simulate post-cracking sliding resistance. The tensile strength across the interface was limited to 0.01 MPa, and minimum normal and tangential stiffness values were defined to ensure numerical stability after interface softening. This interface model captures the nonlinear interaction between steel and concrete, including initial bond behavior, progressive degradation, and residual frictional sliding post-failure. Figure 5 illustrate how material assignments and interface properties were defined in the GiD–ATENA modeling environment.

σ nn f t

K min

nn

K nn

1

1

Δu

Figure 5. Interface model behaviour in shear and tension and model implementation

5. Results The TR01b specimen represents a medium-length bonded anchorage without any mechanical enhancement, serving as a reference case in this study. The ATENA finite element model closely captured the specimen’s behavior up to the peak load. The simulation successfully reflected both the initial elastic stiffness and the shift into the nonlinear hardening phase. It predicted very well the peak load and confirmed that the chosen material models and interface parameters were effective for simulating the anchorage’s overall strength. The simulated post-peak branch displayed a steeper and almost linear decline right after the peak, although in fair accordance with the test (Figure 6). The simulation was able to correctly identify the crack pattern associated to the tensile mechanism, although it did not highlight the splitting cracks occurred at the top concrete surface. Figure 7 presents the results of the TR02a specimen. The ATENA model closely replicates the initial elastic stiffness and matches the experimental trend well throughout the pre-peak region. The numerical simulation well predicts the peak load, reflecting the capability of the fracture–plastic material model and the calibrated interface parameters to accurately represent the load transfer mechanisms involved in the mechanical nut anchorage system. The post-peak phase is simulated only with fair accuracy. The simulation correctly matched the conical breakout failure crack pattern. The results of the TR02b specimen are presented in Figure 8. The ATENA simulation reproduced the experimental response with good accuracy throughout both the pre-peak and peak phases. Of particular interest is the similarity