A data-driven approach for predicting stress intensity factors of a single-edge cracked plate with a random polygon-shaped void

Mehrad Zargar Ershadi; Saeid Nickabadi; Majid Askari Sayar; Alireza Alidoust; Reza Ansari

doi:10.59400/mea3338

A data-driven approach for predicting stress intensity factors of a single-edge cracked plate with a random polygon-shaped void

Mehrad Zargar Ershadi
Faculty of Mechanical Engineering, University of Guilan, Rasht P.O. Box 3756, Iran
Saeid Nickabadi
Faculty of Mechanical Engineering, University of Imam Khomeini Marine Sciences, Nowshahr 4651783311, Iran
Majid Askari Sayar
Faculty of Mechanical Engineering, University of Imam Khomeini Marine Sciences, Nowshahr 4651783311, Iran
Alireza Alidoust
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
Reza Ansari
Faculty of Mechanical Engineering, University of Guilan, Rasht P.O. Box 3756, Iran

Article ID: 3338

Keywords: machine learning algorithms, stress intensity factor, computational fracture mechanics, data-driven approach, polygon-shaped voids

Abstract

This study represents a data-driven framework for predicting mode I (K_I) and mode II (K_II) Stress Intensity Factors (SIFs) in single-edge cracked plates with central polygon-shaped voids. Finite element simulations were conducted in Abaqus software to generate a dataset by varying key parameters, including the polygon’s number of vertices, angle, average radius, and crack length. Two machine learning models were employed to analyze the dataset created by the finite element method: Group Method of Data Handling (GMDH) networks and an Artificial Neural Network (ANN). The GMDH networks were optimized using the least squares method and the Root Mean Squared Error (RMSE) criteria, while the ANN, designed as a feedforward fully connected network, was trained with the backpropagation algorithm and the gradient descent optimization technique using TensorFlow and Keras libraries. The ANN demonstrated exceptional accuracy, with a R² value exceeding 0.99 for K_Ipredictions and 0.98 for K_II, significantly outperforming GMDH models, particularly in capturing the nonlinear behavior of K_II.

Published

2025-12-03

How to Cite

Zargar Ershadi, M., Nickabadi, S., Sayar, M. A., Alidoust, A., & Ansari, R. (2025). A data-driven approach for predicting stress intensity factors of a single-edge cracked plate with a random polygon-shaped void. Mechanical Engineering Advances, 3(4). https://doi.org/10.59400/mea3338

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Vol. 3 No. 4 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Sumpter JDG, Kent JS. Prediction of ship brittle fracture casualty rates by a probabilistic method. Marine Structures. 2004; 17(8): 575–589. doi: 10.1016/J.MARSTRUC.2005.03.003

[2]Inglis CE. Stresses in a plate due to the presence of cracks and sharp corners. Transactions of the Institution of Naval Architects. 1913; 55: 219–241.

[3]Griffith AA. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character. 1921; 221: 163–198.

[4]Ibrahim RA. Overview of structural life assessment and reliability, part I: Basic ingredients of fracture mechanics. Journal of Ship Production and Design. 2015; 31(1): 1–42. doi: 10.5957/JSPD.2015.31.1.1

[5]Ferrian F, Cornetti P, Sapora A, et al. Crack tip shielding and size effect related to parallel edge cracks under uniaxial tensile loading. International Journal of Fracture. 2024; 245(3): 223–233. doi: 10.1007/S10704-023-00756-1

[6]Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics. 1968; 35(2): 379–386. doi: 10.1115/1.3601206

[7]Li Y, Ni T, Zhang F, et al. U-Net learning for the automatic identification of the sandstone crack tip position to determine mixed-mode stress intensity factors utilizing digital image correlation method. Theoretical and Applied Fracture Mechanics. 2023; 127: 104028. doi: 10.1016/J.TAFMEC.2023.104028

[8]Xiao H, Xie Y, Yue Z. Analysis of square-shaped crack in layered halfspace subject to uniform loading over rectangular surface area. Computer Modeling in Engineering and Sciences. 2015; 109–110(1): 55–80. doi: 10.3970/CMES.2015.109.055

[9]Kumar SS, Prakash RV. Stress intensity factor solution for a naturally emanating crack out of a V-notched round bar. International Journal for Computational Methods in Engineering Science and Mechanics. 2015; 16(5): 301–312. doi: 10.1080/15502287.2015.1080319

[10]Fardaghaie A, Shahrooi S, Shishehsaz M. A novel correlation to calculate stress intensity factors of the semi-elliptical crack in high-strength carbon steel pipe based on extended isogeometric analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2022; 44(1): 50. doi: 10.1007/S40430-021-03343-4

[11]Tang SB. Stress intensity factors for a Brazilian disc with a central crack subjected to compression. International Journal of Rock Mechanics and Mining Sciences. 2017; 93: 38–45. doi: 10.1016/J.IJRMMS.2017.01.003

[12]Dong S. Theoretical analysis of the effects of relative crack length and loading angle on the experimental results for cracked Brazilian disk testing. Engineering Fracture Mechanics. 2008; 75(8): 2575–2581. doi: 10.1016/J.ENGFRACMECH.2007.09.008

[13]Hassani Niaki M, Pashaian M. Using deep learning method to predict dimensionless values of stress intensity factors and T-stress of edge notch disk bend specimen. Fatigue and Fracture of Engineering Materials and Structures. 2024; 47(8): 2789–2802. doi: 10.1111/FFE.14330

[14]Bert CW, Malik M. Differential quadrature: a powerful new technique for analysis of composite structures. Composite Structures. 1997; 39(3–4): 179–189.

[15]Kabir H, Aghdam MM. A generalized 2D Bézier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets. Thin-Walled Structures. 2021; 169: 108484.

[16]Coelho JS, Machado MR, Dutkiewicz M, et al. Data-driven machine learning for pattern recognition and detection of loosening torque in bolted joints. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2024; 46(2): 75. doi: 10.1007/S40430-023-04628-6

[17]Zheng M, Yu J. Parametric optimization and determination in machining processes by means of probabilistic multi-objective optimization. Mechanical Engineering Advances. 2025; 3(1). doi: 10.59400/MEA1950

[18]Moore BA, Rougier E, O’Malley D, et al. Predictive modeling of dynamic fracture growth in brittle materials with machine learning. Computational Materials Science. 2018; 148: 46–53. doi: 10.1016/J.COMMATSCI.2018.01.056

[19]Jiang S, Du J, Wang S, et al. Risk assessment of initial crack propagation in bearing steel based on finite element analysis and machine learning. Mechanics Based Design of Structures and Machines. 2024; 53(5): 3619–3634. doi: 10.1080/15397734.2024.2429738

[20]Kim KB, Yoon DJ, Jeong JC, et al. Determining the stress intensity factor of a material with an artificial neural network from acoustic emission measurements. NDT and E International. 2004; 37(6): 423–429. doi: 10.1016/J.NDTEINT.2003.08.007

[21]Liu X, Athanasiou CE, Padture NP, et al. A machine learning approach to fracture mechanics problems. Acta Materialia. 2020; 190: 105–112. doi: 10.1016/J.ACTAMAT.2020.03.016

[22]Talebi H, Bahrami B, Daneshfar M, et al. Data-driven based fracture prediction of notched components. Philosophical Transactions of the Royal Society A. 2024; 382(2264): 20220397. doi: 10.1098/RSTA.2022.0397

[23]Kaloop MR, Samui P, Kim JJ, et al. Stress intensity factor prediction on offshore pipelines using surrogate modeling techniques. Case Studies in Construction Materials. 2022; 16: e01045. doi: 10.1016/J.CSCM.2022.E01045

[24]Zhang X, Zhao T, Liu Y, et al. A data-driven model for predicting the mixed-mode stress intensity factors of a crack in composites. Engineering Fracture Mechanics. 2023; 288: 109385. doi: 10.1016/J.ENGFRACMECH.2023.109385

[25]Parsania A, Kakavand E, Hosseini SA, et al. Estimation of multiple cracks interaction and its effect on stress intensity factors under mixed load by artificial neural networks. Theoretical and Applied Fracture Mechanics. 2024; 131: 104340. doi: 10.1016/J.TAFMEC.2024.104340

[26]Williams ML. On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics. 1957; 24(1): 109–114. doi: 10.1115/1.4011454

[27]Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics. 1957; 24(3): 361–364. doi: 10.1115/1.4011547

[28]Tada H, Paris PC, Irwin GR. The Stress Analysis of Cracks Handbook, 3rd ed. ASME Press; 2000. doi: 10.1115/1.801535

[29]ASTM International Committee E08 on Fatigue and Fracture. Standard Test Method for Linear-elastic Plane-strain Fracture Toughness KIC of Metallic Materials. ASTM International; 2013.

[30]Algorithm to generate random 2D polygon. Available online: https://stackoverflow.com/questions/8997099/algorithm-to-generate-random-2d-polygon (accessed on 10 December 2024).

[31]Rezasefat M, Hogan JD. A finite element-convolutional neural network model (FE-CNN) for stress field analysis around arbitrary inclusions. Machine Learning: Science and Technology. 2023; 4(4): 045052. doi: 10.1088/2632-2153/AD134A

[32]Alshoaibi AM, Ariffin AK. Finite element simulation of stress intensity factors in elastic-plastic crack growth. Journal of Zhejiang University SCIENCE A. 2006; 7(8): 1336–1342. doi: 10.1631/JZUS.2006.A1336

[33]Rao BN, Rahman S. A coupled meshless-finite element method for fracture analysis of cracks. International Journal of Pressure Vessels and Piping. 2001; 78(9): 647–657. doi: 10.1016/S0308-0161(01)00076-X

[34]Yan X. An empirical formula for stress intensity factors of cracks emanating from a circular hole in a rectangular plate in tension. Engineering Failure Analysis. 2007; 14(5): 935–940. doi: 10.1016/J.ENGFAILANAL.2006.11.008

[35]Ivakhnenko AG. Heuristic self-organization in problems of engineering cybernetics. Automatica. 1970; 6(2): 207–219. doi: 10.1016/0005-1098(70)90092-0

[36]Ivakhnenko AG. Polynomial theory of complex systems. IEEE Transactions on Systems, Man, and Cybernetics. 1971; 1(4): 364–378. doi: 10.1109/TSMC.1971.4308320

[37]Madandoust R, Bungey JH, Ghavidel R. Prediction of the concrete compressive strength by means of core testing using GMDH-type neural network and ANFIS models. Computational Materials Science. 2012; 51(1): 261–272. doi: 10.1016/J.COMMATSCI.2011.07.053

[38]Panoiu M, Panoiu C, Rusu-Anghel S, et al. Modeling the pantograph-catenary contact in electric railway transportation using group method of data handling. In: Proceedings of the IECON Industrial Electronics Conference; 14–17 October 2019; Lisbon, Portugal. doi: 10.1109/IECON.2019.8927244

[39]Mostapha Kalami Heris. Group Method of Data Handling (GMDH) in MATLAB. Available online: https://yarpiz.com/263/ypml113-gmdh (accessed on 5 May 2025).

[40]Hosseinian SM, Bazoobandi P, Mousavi SR, et al. Presentation of machine learning methods and multi-objective optimization of fracture indices for asphalt rubber mixtures containing wax-based warm mix additives modified by nano calcium carbonate. Construction and Building Materials. 2023; 409: 134136. doi: 10.1016/J.CONBUILDMAT.2023.134136

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