Issue 78

A. Gallo et alii, Fracture and Structural Integrity, 78 (2026) 489-503; DOI: 10.3221/IGF-ESIS.78.28

improvement obtained using the algorithm. The duration of optimization process was 7 hours and 13 minutes, carried out in 7 iterations on the same workstation configuration.

Optimized with LM

Optimized with MBS

Reference

41000

41000

41000

E [MPa]

0.35

0.35

0.35

ν [-]

221.00

221.01

261.31

σ S [MPa]

1.5 1.0

1.5 1.0

1.5 1.0

q 1 [-] q 2 [-] q 3 [-] n [-] f 0 [-] f N [-] S N [-] ε N [-] f c [-] f f [-] F [-]

2.25 0.10

2.25

2.25 0.13

0.1797 0.00001 0.1152 0.2969 0.0720 0.3317 0.4822 0.0252

0.0005

0.0031

0.04 0.15

0.053

0.27

0.3

0.207

0.35

0.15 0.35

0.5

0.2488

0.0098

Table 2: Identified GTN parameters.

Figure 5 : Experimental and GTN optimal numerical stress-strain curves for ZK60 alloy The sound enforcement of constraints confirms the effectiveness of the interior penalty function approach in handling the strong coupling and hierarchical nature of GTN parameters. Differently, the standard Newton scheme ( ൌ 1 ) without Wolfe conditions and NLS diverged after only one iteration and failed to identify a descent direction. An alternative optimization strategy based on the LM algorithm was also investigated. Although this method successfully reduced the objective function, after 23 hours of computation and 15 iterations, the minimum value achieved for F was about 0.025, one order of magnitude higher than that obtained with MBS, while also requiring significantly greater computational effort. It is worth noting that the lower objective-function value obtained with MBS shows better agreement with the selected experimental curve used for parameter identification. However, because GTN parameters are derived from a single stress strain curve, this result does not provide uniqueness or superior physical identifiability of the obtained parameters, although

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