PSI - Issue 66
Domenico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 320–330 Author name / Structural Integrity Procedia 00 (2025) 000–000
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Table 1. TPB test results in terms of peak load predicted by MNS and related percentage error with respect to DNS. max F (kN) error (%) MNS (Delaunay triangular mesh) 1.035 -0.36 MNS (cross-triangle quadrilateral mesh) 1.034 -0.48 DNS 1.039 -
Furthermore, as shown in Figs. 5(a) and (b), the proposed multiscale approach is able to predict also mesh independent results in terms of overall crack trajectories. In particular, the adopted of the cross-triangle mapped mesh leads to a perfectly straight crack path, being coherent with the assumed Mode-I fracture conditions at the macroscale (see Fig. 5(b)). Instead, the use of a random mesh induces an artificial crack tortuosity, which is however only a local deviation respect to the average straight path (see Fig. 5(a)). Interestingly, in the latter case, the resulting overestimation of the macroscopic crack length does not lead to an analogous overestimation of the fracture energy, by virtue of the “on-the-fly” adjustments of the overall Traction-Separation Law (TLS) provided by the proposed cohesive/bulk homogenization scheme. In other words, the proposed approach is able to potentially overcome the artificial toughening effect induced by crack path tortuosity, which typically affects most of the existing cohesive/volumetric finite element approaches unless using special moving mesh strategies (like those presented in Pascuzzo et al. (2022a), Ammendolea et al. (2023a), Ammendolea et al. (2023b), Ammendolea et al. (2023c), De Maio et al. (2024)).
Fig. 5. TPB test results in terms of crack trajectory predicted by the Multiscale Numerical Simulation (MNS) for different discretizations: (a) Delaunay triangular mesh; (b) cross-triangle quadrilateral mesh.
Finally, the analysis of computational performances provided by the proposed multiscale approach is presented in Table 2. In particular, the CPU times required by the present two Multiscale Numerical Simulations (with random and mapped meshes) are compared with those associated with the (reference) Direct Numerical Simulation. The resulting speed-up values (about 40 in both cases) confirm the high computational efficiency of the proposed hybrid cohesive/bulk homogenization scheme. This is essentially due to the notable decrease in the number of degrees of freedom for the associate macroscopic mesh.
Table 2. TPB test results in terms of CPU time required by MNS and related speed-up with respect to DNS. CPU time Speed-up MNS (Delaunay triangular mesh) 1min 44s 43.54 MNS (cross-triangle quadrilateral mesh) 2min 1s 37.42 DNS 1h 15min 28s -
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