Issue 78

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

⎪⎧ ൌ ln ൬ ௤ାଵ െ ௤ െ ൰ ln ൬ ௤ାଵ ௤ ൰ ൌ ௤ െ ௣௟ , ௡ ௤

ቊ ௤ ൌ ൅ ௣௟ , ௖ ௤ ௤ାଵ ൌ ൅ ௣௟ , ௖ ௤ାଵ ⇒ ⎪⎩ ⎨ ⎪

where q denotes the number of points extrapolated from the experimental curve that was set equal to 100. This procedure returned a set of െ 1 pairs of and values. The initial guess was then determined as the mean of the aforementioned pairs of values, and ሺ ሻ was calculated using eq. (14). The optimized solution is reached in 22 minutes and 5 iterations on a workstation equipped with an Intel core i9 (24 cores) CPU and 128 GB of RAM. A comparison of experimental and optimized numerical stress-strain curves is presented in Fig. 4, showing a satisfactory agreement. Moreover, results also confirm that maintaining the elastic properties unchanged does not affect the accuracy of the plastic calibration, although significantly simplifies the optimization procedure.

Figure 4 : Comparison of experimental and JC optimized numerical stress-strain curves for ZK60 alloy In order to assess the effectiveness of the optimization strategy, some well-established algorithms from the literature were considered for comparison. First, a classical Newton method with a fixed step size ( α = 1) and without Wolfe line-search conditions was applied to the same identification problem. Under the same initial conditions, the algorithm diverged after only two iterations, demonstrating poor robustness for this highly nonlinear optimization problem. Instead, the conventional Newton method with a line-search (NLS) converged in 33 minutes and 12 iterations, obtaining an objective function value about 33% higher than that resulted by MBS, as shown in Tab. 1. Furthermore, the Levenberg–Marquardt [3,8] and Trust-Region [7,14,18,19] methods were also investigated. Starting from the same initial guess (Reference 2 in Tab. 1), the LM algorithm successfully converged closely to parameter values obtained with the developed approach (see Tab. 1). However, the computational cost was significantly higher, requiring approximately 135 minutes and employing 15 iterations, which is about five times longer than the execution time of proposed method and a factor of three increase in the number of iterations. In contrast, the TR method exhibited a prolonged stagnation phase, remaining trapped for about eight iterations in a region far from the optimal solution. Although the algorithm eventually escaped this region and converged to value of F equal to 0.0359, the overall computational effort was considerably larger, exceeding four hours of execution time. For this reason, the TR approach was avoided in the following test cases. A sensitivity analysis was also performed to assess the computational cost and solution accuracy for values of ψ equal to 0.9, 0.8, and 0.7, using the same initial guesses. For ψ = 0.9 the algorithm carried out an objective function value of F = 0.00698 after 3 iterations, with a computation time of 23 minutes. For ψ = 0.8, the previous value of F was obtained after 2 iterations,

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