PSI - Issue 66

Gabriele Cricrì et al. / Procedia Structural Integrity 66 (2024) 82–86 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Figure 2 shows the crack paths predicted by the two models against the experimental results. The computed crack profiles do match quite well with the experiment for the two methods. In particular, in the global energy approach the computed crack paths do not change their curvature, are uniformly convergent with the size of the increment ∆ and tend to reach the middle of the experimental data range, thereby reproducing well the experiment. On the other side, the skeleton of the fully damaged region that is obtained with the graded damage model is located in the lower part of the experimental data range, it exhibits a curvature change and remains almost unchanged when the length scale parameter ℓ decreases from 10 mm to 5 mm.

Fig. 3. L-shaped panel. Computed VS experimental load-displacement curves. Figure 3 illustrates the reaction forces from the simulations and the corresponding experimental data. The Griffith like model provides an unbounded maximum reaction force for vanishing ∆ , which is not surprising since this model does not contain the crack initiation. Contrariwise, the response obtained using the graded damage model agrees well with the experiment, as it is able to capture the peak load and the shape of the experimental curve. Moreover, the global response of the damage model is not insensitive with respect to the regularizing factor ℓ , which suggests that the length scale plays the role of a true material parameter. 5. Closure We presented a comparison between two methods for the simulation of fracture in elastic solids. Though substantially different, the numerical results obtained for a representative test problem are comparable each other. More specifically, the crack paths obtained using the global energy minimization look coherent and much more regular than the one emanating from the graded damage approach. Contrariwise, the experimental load-displacement data range is well captured only using the continuum damage model whereas the global energy approach does not do the job. In a sense this is not surprising since a Griffith-like model with a single material parameter, i.e. the critical fracture energy, cannot reproduce the full response of a quasi-brittle material. References Valoroso, N., Stolz, C., 2022. Graded damage in quasi-brittle solids. International Journal for Numerical Methods in Engineering 123(11), 2467– 2498. https://doi.org/10.1002/nme.6947. Cricrì, G., 2024. On the determination of the quasi-static evolution of brittle plane cracks via stationarity principle. Computer Methods in Applied Mechanics and Engineering 425, 116941. https://doi.org/10.1016/j.cma.2024.116941. Winkler, B.J., 2001. Traglastuntersuchungen von unbewehrten und bewehrten Betonstrukturen auf der Grundlage eines objektiven Werkstoffgesetzes für Beton (PhD thesis), Innsbruck University Press.