Issue 78

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

formulation. In contrast, the shape optimization case study is formulated using a generic structural steel material. This choice allows for the evaluation of the optimization algorithm independently of material-specific nonlinearities in multivariable optimization context. Consequently, this example complements the material model calibration problems by demonstrating the applicability of the developed method to structural optimization tasks, where the objective function depends on the global structural response rather than on constitutive parameter estimations. The effectiveness of MBS methodology is assessed through comparisons with standard Newton schemes, first-order methods, Levenberg-Marquardt (LM) and Trust Region (TR) algorithms. For all analysed benchmark problems, it consistently identifies the target minima with fewer iterations and lower computational times while maintaining constraint satisfaction. Additional details on the material behaviour, experimental background, and modelling assumptions are provided in the corresponding subsections.

Figure 1: Scheme of MBS algorithm.

N UMERICAL SIMULATION AND RESULTS

Calibration of Johnson-Cook model he first case study deals with the calibration of the Johnson-Cook (JC) plasticity model [23,24], which is widely adopted to describe the strain, strain-rate, and temperature-dependent behaviour of metallic materials under large deformations. The JC formulation expresses the flow stress as a multiplicative function of equivalent plastic strain ௣௟ , plastic strain rate ሶ ௣௟ , and homologous temperature, and is characterized by five parameters controlling yield strength, T

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