PSI - Issue 39

Umberto De Maio et al. / Procedia Structural Integrity 39 (2022) 677–687 Author name / Structural Integrity Procedia 00 (2019) 000–000

684

8

DIM

2.1

2.97

125

1250

5.63e14

2.81e14

Moreover, in order to avoid the preferential crack paths, the cohesive elements are not inserted along the straight lines coinciding with both vertical and horizontal truss elements. The material parameters for the cohesive interfaces are listed in Table 3. A novelty aspect of the present study is the adoption of a new path-following scheme able to overcome the limitations of classical displacement-controlled Newton-Raphson solution algorithms, which usually fail to trace the unstable branches of the equilibrium path during the failure of the structural elements (as shown in many works, such as De Maio et al. (2020d); Greco et al. (2021b), (2020b) Lonetti et al. (2019) in the context of the geometrically nonlinear analysis of composite materials and network arch bridges, respectively). In particular, in the present work, a general hybrid path-following scheme for the cohesive fracture analysis is obtained from the synergistic combination of a classical displacement control and a newly proposed continuation strategy which adopts as a continuation parameter the average value of the normal displacement jump over all the cohesive interfaces. The switching criterion between the two adopted path-following schemes is based on the number of Newton-Raphson iterations. The numerically predicted structural response of the tested FRP-plated RC beam is reported in Figure 8, in terms of loading curve, together with the reference experimental results obtained in Gao et al. (2004).

Fig. 8. Load versus deflection curve obtained by the proposed model together with the experimental outcomes.

The curve predicted by the present numerical model is in good agreement with the experimental outcomes, especially in terms of both peak and residual behaviors. It is worth noting that, until the peak load (point B of Figure 8) is reached, the numerical results have been obtained by means of a classical displacement control, being the structural response stable. At point B, coinciding with the onset of the debonding mechanism, once the number of Newton-Raphson iterations has reached a critical threshold, the proposed hybrid path-following scheme switches from the displacement control to the previously mentioned average displacement jump control. In this way, it is possible to follow the snap-back branch of the equilibrium path, characterized by a severe reduction of both the load-carrying capacity and the beam deflection (up to the limit point C). After this, a strength recovery is experienced up to the achievement of its final residual value (Point D), coinciding with the ultimate strength of the beam without the FRP system (in good agreement with that obtained in Gao et al. (2004)). Figure 9 shows the main crack patterns for different notable points along the post-peak branch of the equilibrium curve shown in Figure 8 (points A, B, C and D). The adopted inter-element fracture approach allows the diffuse damage typical of reinforced concrete beams to be correctly captured together with the delamination of the FRP plate reinforcement from the concrete beam in a very realistic manner. Finally, through the embedded truss model, used in