PSI - Issue 68

ScienceDirect Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2025) 000–000 Available online at www.sciencedirect.com Procedia Structural Integrity 68 (2025) 1312–1318 Structural Integrity Procedia 00 (2025) 000–000

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European Conference on Fracture 2024 An innovative solution for determining stress intensity factors (SIF) using the GMDH neural network Morteza Khomami Abadi a , Mohammad Zaman Kabir a, *, Kamran Nikbin b a Department of Civil and Environmental Engineering, Amirkabir University of Technology, Hafez Ave 15875, Tehran, Iran b Department of Mechanical Engineeing, Imperial College London, London, SW72AZ, UK Abstract The Stress Intensity Factor, SIF, is a conventional index to assess the elastic stress state at the tip of a mathematically sharp crack in fracture mechanics and also is an appropriate quantity for crack opening and fracture development in brittle materials. This paper presents a statistical solution based on the Group Method of Data Handling, GMDH, to determine the stress intensity fac-tors (KI). The results of this method are compared and validated with the previous analytical and numerical methods. In order to extract the SIFs, a certain number of tests were performed by changing the geometrical parameters, boundary and loading conditions using DOF (Design of Experiments) method. Each experiment is independently simulated in the Abaqus software and the values of stress intensity factors are calculated. The inputs of each test, including geometric dimensions, crack location, crack depth, boundary conditions and loading situation, along with the test output, are introduced to the GMDH algorithm. The best and most optimal connection between the inputs and outputs by considering the lowest error was set after processing the data in the algorithm. In this study, the stress intensity factors are calculated for beams under bending moment and transverse loading and plates containing two types of crack; single-edge crack and central crack. The accuracy of the presented statistical method is validated by J-integral method in Abaqus software. The comparison of the results from the current study with those obtained using existing the analytical and numerical methods are satisfied with less than 8.4% differences. It is known that there are limitations in the analytical method for crack depth (a/L>0.7). However, the statistical approach is strong enough to provide solutions for deep cracks. The main advantage of this method, based on the neural network, is its flexibility and versatility for any types of geometric, material property, loading and boundary conditions. Keywords: Stress intensity factors; Neural network; GMDH; Crack; Fracture; Abaqus European Conference on Fracture 2024 An innovative solution for determining stress intensity factors (SIF) using the GMDH neural network Morteza Khomami Abadi a , Mohammad Zaman Kabir a, *, Kamran Nikbin b a Department of Civil and Environmental Engineering, Amirkabir University of Technology, Hafez Ave 15875, Tehran, Iran b Department of Mechanical Engineeing, Imperial College London, London, SW72AZ, UK Abstract The Stress Intensity Factor, SIF, is a conventional index to assess the elastic stress state at the tip of a mathematically sharp crack in fracture mechanics and also is an appropriate quantity for crack opening and fracture development in brittle materials. This paper presents a statistical solution based on the Group Method of Data Handling, GMDH, to determine the stress intensity fac-tors (KI). The results of this method are compared and validated with the previous analytical and numerical methods. In order to extract the SIFs, a certain number of tests were performed by changing the geometrical parameters, boundary and loading conditions using DOF (Design of Experiments) method. Each experiment is independently simulated in the Abaqus software and the values of stress intensity factors are calculated. The inputs of each test, including geometric dimensions, crack location, crack depth, boundary conditions and loading situation, along with the test output, are introduced to the GMDH algorithm. The best and most optimal connection between the inputs and outputs by considering the lowest error was set after processing the data in the algorithm. In this study, the stress intensity factors are calculated for beams under bending moment and transverse loading and plates containing two types of crack; single-edge crack and central crack. The accuracy of the presented statistical method is validated by J-integral method in Abaqus software. The comparison of the results from the current study with those obtained using existing the analytical and numerical methods are satisfied with less than 8.4% differences. It is known that there are limitations in the analytical method for crack depth (a/L>0.7). However, the statistical approach is strong enough to provide solutions for deep cracks. The main advantage of this method, based on the neural network, is its flexibility and versatility for any types of geometric, material property, loading and boundary conditions. Keywords: Stress intensity factors; Neural network; GMDH; Crack; Fracture; Abaqus © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers

* Corresponding author. Tel.: +98 (21) 64543032; fax: +98 (21) 64543032. E-mail address: mzkabir@aut.ac.ir

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers 10.1016/j.prostr.2025.06.204 2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers 2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers * Corresponding author. Tel.: +98 (21) 64543032; fax: +98 (21) 64543032. E-mail address: mzkabir@aut.ac.ir