Issue 78

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

A second-order relaxed Newton framework for material parameters identification and stress-constrained structural optimization

Antonio Gallo, Enrico Armentani Department of Chemical, Materials and Industrial Production Engineering, University of Napoli Federico II, Napoli, 80125, Italy antonio.gallo2@unina.it, http://orcid.org/0009-0001-2171-418X enrico.armentani@unina.it, http://orcid.org/0000-0002-3511-6121 Michele Ferraiuolo CIRA – Italian Aerospace Research Centre, via Maiorise snc, 81043 Capua, CE, Italy m.ferraiuolo@cira.it, https://orcid.org/0000-0002-3200-321X Michele Perrella Department of Chemical, Materials and Industrial Production Engineering, University of Napoli Federico II, Napoli, 80125, Italy michele.perrella@unina.it, https://orcid.org/0000-0002-3617-2328

Citation: Gallo, A., Armentani, E., Ferraiuolo, M., Perrella, M., A second-order relaxed Newton framework for material parameters identification and stress constrained structural optimization, Fracture and Structural Integrity, 78 (2026) 489-503.

A BSTRACT . This work presents the development and implementation of a second-order optimization algorithm based on a relaxed Newton method for the minimization of nonlinear scalar objective functions with multiple design variables. The proposed strategy combines a modified Newton scheme with a customized backtracking formulation, which explicitly enforces the Armijo sufficient decrease condition to improve convergence and stability in highly nonlinear problems and reduce computational cost. A refinement parameter is introduced to generalize the step-size sequence into a continuous form, providing a relaxation of the standard backtracking scheme. Unlike standard tuning parameters, it acts directly on the mathematical structure of the line search procedure and remains independent of the specific physical problem, constitutive model, or objective function. The methodology is assessed through three case studies of increasing complexity, namely calibration of the Johnson–Cook plasticity model, calibration of the Gurson– Tvergaard– Needleman ductile damage model, and stress-constrained shape optimization of a hollow plate. The results demonstrate accurate parameter identification, robustness to initial guesses, and effective handling of both equality and inequality constraints through Lagrange multipliers and interior penalty

Received: 17.07.2026 Accepted: 16.09.2026 Published: 21.09.2026 Issue: 10.2026

Copyright: © 2026 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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