PSI - Issue 66

Domentico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 350–361 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 4. Computational meshes adopted in numerical simulations. (a) Direct analysis (b) Multiscale analyses

Besides, the results denote that the proposed method significantly reduces computational time spent to perform numerical simulations (see Fig. 5-b). In particular, the reduction compared to DA is about 66%, 74%, and 81% for MSA developed by assuming  equals 1, 1.2, and 1.4. Such results indicate that the proposed adaptive multiscale model is accurate and computationally efficient. Fig. 6 shows a schematic of the phase field distribution for the value of the vertical force  associated with the peak force in Fig. 5-a. The results of the DA are compared with those obtained from MSA. As expected, the damage zone develops around the midspan of the beam, and, in such a context, the maps of the damage predicted by MSA analyses are equivalent to that obtained by DA. Besides, it is expected that the extremities of the beam are unaffected by damage, thus remaining in a linear-elastic regime. Such behavior is confirmed in DA by the small value of the phase field variable (f) and in MSA results by the presence of coarse regions. When comparing the results of MSA analyses, it becomes clear that using larger-scale factor values can have a beneficial effect. Specifically, when larger values  are adopted, the refinement of coarser regions that are moderately affected by damage mechanisms does not occur.

Fig. 5. (a) A comparison between DA and MSA in terms of (a) vertical displacement of the top midspan point of the beam (  ) versus applied force ( F ) and (b) computational time spent to perform the numerical simulations.