Paper ID: 1576

Stress Distribution Prediction in front of the crack tip using Artificial Neural Networks: A Data-Driven Approach in Fracture Mechanics

 

Khairul Anam1,*, Anindito Purnowidodo1, Pavan Kumar Asur Vijaya Kumar2, 3, Heinz E. Pettermann2

1Department of Mechanical Engineering, Engineering Faculty, Brawijaya University, MT Haryono167 Malang 65145, Indonesia

2Institute of Lightweight Design and Structural Biomechanics, TU Wien, Getreidemarkt 9, 1060 Wien, Austria

3Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

 

*Corresponding author: khairul.anam27@ub.ac.id

 

Abstract

Understanding the stress distribution in front of the crack tip is essential because this region experiences high stress concentration that can control crack initiation and propagation. This study proposes an artificial neural network (ANN) model as a computationally efficient surrogate model for predicting the stress distribution and stress values in front of the crack tip in a simple cracked geometry. The proposed ANN model complements conventional finite element method (FEM) analyses by enabling rapid stress prediction once the model has been trained. The results show that the ANN model can capture the general relationship between the stress intensity factor, radial distance, angular position, and crack-tip stress. However, its predictive performance strongly depends on the magnitude of the stress intensity factor. At low K values, the ANN model shows significant discrepancies in both stress values and contour visualization, and it cannot accurately reproduce the theoretical butterfly-shaped stress distribution. At higher K values, the predicted stress distribution is closer to the analytical solution, and the contour shape is more consistent. These findings indicate that the present ANN model should be regarded as a proof-of-concept surrogate model with limitations, rather than a replacement for analytical LEFM solutions or FEM analysis.

Keywords: artificial neural network; crack tip; finite element method; prediction; stress distribution.

References

Al-Hussein, W. A., Por, L. Y., Kiah, M. L. M., & Zaidan, B. B. (2022). Driver Behaviour Profiling and Recognition Using Deep-Learning Methods: In Accordance with Traffic Regulations and Experts Guidelines. International Journal of Environmental Research and Public Health, 19(3), 1470. https://doi.org/10.3390/ijerph19031470

Anderson, T. L. (2017). Fracture mechanics: fundamentals and applications. Crc Press/Taylor & Francis.

Barbosa, J. F., Correia, J. A. F. O., Freire, J. R. C. S., & Abílio, J. (2020). Fatigue life prediction of metallic materials considering mean stress effects by means of an artificial neural network. International Journal of Fatigue, 135, 105527. https://doi.org/10.1016/j.ijfatigue.2020.105527

Chen, Z., Dai, Y., & Liu, Y. (2023). Life prediction of corrosion fatigue based on a new crack growth rate model with damage and the extended finite element method. Engineering Fracture Mechanics, 289, 109445. https://doi.org/10.1016/j.engfracmech.2023.109445

Dowling, N. E., Katakam Siva Prasad, & R Narayanasamy. (2013). Mechanical behaviour of materials: engineering methods for deformation, fracture, and fatigue. Pearson; Harlow.

Giner, E., Sukumar, N., Denia, F. D., & Fuenmayor, F. J. (2008). Extended finite element method for fretting fatigue crack propagation. International Journal of Solids and Structures, 45(22), 5675–5687. https://doi.org/10.1016/j.ijsolstr.2008.06.009

Gu, Y., Zhang, C., Zhang, P., & Golub, M. V. (2023). Enriched physics-informed neural networks for in-plane crack problems: Theory and MATLAB codes. International Journal of Solids and Structures, 276, 112321. https://doi.org/10.1016/j.ijsolstr.2023.112321

Gupta, S., Xin, H., & Veljkovic, M. (2019). Fatigue crack propagation simulation of orthotropic bridge deck based on extended finite element method. First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019), 22, 283–290. https://doi.org/10.1016/j.prostr.2020.01.036

Hutař, P., Ševčík, M., Náhlík, L., Zouhar, M., Seitl, S., Knésl, Z., & FernándezCanteli, A. (2010). Fracture mechanics of the threedimensional crack front: vertex singularity versus out of plain constraint descriptions. Fatigue 2010, 2(1), 2095–2102. https://doi.org/10.1016/j.proeng.2010.03.225

Kazeruni, M., & Ince, A. (2023). Datadriven artificial neural network for elastic plastic stress and strain computation for notched bodies. Theoretical and Applied Fracture Mechanics, 125, 103917. https://doi.org/10.1016/j.tafmec.2023.103917

Khaleghi, M., Haghighat, E., Vahab, M., Shahbodagh, B., & Khalili, N. (2022). Fracture characterization from noisy displacement data using artificial neural networks. Engineering Fracture Mechanics, 271, 108649. https://doi.org/10.1016/j.engfracmech.2022.108649

Khatir, A., Capozucca, R., Khatir, S., Magagnini, E., Le Thanh, C., & Riahi, M. K. (2025). Advancements and emerging trends in integrating machine learning and deep learning for SHM in mechanical and civil engineering: A comprehensive review. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 47(9), Article 419. https://doi.org/10.1007/s40430-025-05697-5

Khatir, A., Capozucca, R., Khatir, S., & Magagnini, E. (2022). Vibration-based crack prediction on a beam model using hybrid butterfly optimization algorithm with artificial neural network. Frontiers of Structural and Civil Engineering, 16(8), 976–989. https://doi.org/10.1007/s11709-022-0840-2

Khatir, A., Oulad Brahim, A., Capozucca, R., Khatir, S., Noori, M., Sarhosis, V., Bhowmik, B., & Cuong-Le, T. (2026). Structural recovery and damage prediction in GFRP-BFRP patched plates using hybrid SSA-SCA-XGBoost model and vibration data. Composite Structures, 393, 120638. https://doi.org/10.1016/j.compstruct.2026.120638

Khoei, A. R., Moslemi, H., & Seddighian, M. R. (2020). An efficient stress recovery technique in adaptive finite element method using artificial neural network. Engineering Fracture Mechanics, 237, 107231. https://doi.org/10.1016/j.engfracmech.2020.107231

Logan, D. L. (2016). A first course in finite element method: sixth edition. Cengage Learning.

Ma, X., He, X., & Tu, Z. C. (2021). Prediction of fatigue–crack growth with neural networkbased increment learning scheme. Engineering Fracture Mechanics, 241, 107402. https://doi.org/10.1016/j.engfracmech.2020.107402

Makabe, C., Purnowidodo, A., & McEvily, A. J. (2004). Effects of surface deformation and crack closure on fatigue crack propagation after overloading and underloading. International Journal of Fatigue, 26(12), 1341–1348. https://doi.org/10.1016/j.ijfatigue.2004.03.017

Makki, Mhalla, M., & Chokri, Bouraoui. (2017). Experimental, analytical, and finite element study of stress concentration factors for composite materials. Journal of Composite Materials, 51(11), 1583–1594. https://doi.org/10.1177/0021998316659915

Mao, J., Xu, Y., Hu, D., Liu, X., Pan, J., Sun, H., & Wang, R. (2022). Microstructurally short crack growth simulation combining crystal plasticity with extended finite element method. Engineering Fracture Mechanics, 275, 108786. https://doi.org/10.1016/j.engfracmech.2022.108786

Muflikhun, M. A., Putro, A. J. N., Chua, A. Y., & Santos, G. N. C. (2025). Why notch geometry matters for structural and automotive applications: A numerical simulation. Jurnal Rekayasa Mesin, 16(2), 855–880. https://doi.org/10.21776/jrm.v16i2.2095

Nugroho, W. S., Purnami, P., Schulze, A. A., Anggara, A., & Schulze, K. (2025). The prediction of hydrogen evolution reaction from dynamic magnetic field assisted water electrolysis artificial neural network. International Journal of Mechanical Engineering Technologies and Applications (MECHTA), 6(1), 1–10. https://doi.org/10.21776/MECHTA.2025.006.01.1

Nunes, I., Spatti, D. H., Flauzino, R. A., Liboni, L. H. B., & Alves, S. F. R. (2017). Artificial neural networks: A practical course. Springer International Publishing.

Oulad Brahim, A., Khatir, A., Khatir, S., Magagnini, E., Thanh Cuong-Le, & Capozucca, R. (2026). Prediction in percentage variation of frequencies on damaged pipe repaired by composite materials GFRP, CFRP, and BFRP. International Journal of Pressure Vessels and Piping, 222, 105768. https://doi.org/10.1016/j.ijpvp.2026.105768

Prabaswara, I., Sonief, A. A., Hidayati, N. A., & Anam, K. (2023). Finite element analysis on dual small plate and single fixation plate for distal collarbone fracture treatment. International Journal of Mechanical Engineering Technologies and Applications, 4(1), 77–83. https://doi.org/10.21776/mechta.2023.004.01.9

 

Rahmani, M. C., Khatir, A., Azad, M. M., Kim, H. S., Firouzi, N., Kumar, R., Khatir, S., & Cuong, L.-T. (2026). Mechanics-based deep learning framework for predicting deflection of functionally graded composite plates using an enhanced whale optimization algorithm. Mathematics and Mechanics of Solids, 1–22. https://doi.org/10.1177/10812865251398866

Stephens, R. I., Fatemi, A., Stephens, R. R., & Fuchs, H. O. (2001). Metal fatigue in engineering. John Wiley & Sons.  

Tada, H, Irwin, G. R., & Paris, P. C. (2000). The stress analysis of cracks handbook. ASME Press.

Tinoco, H. A., Cardona, C. I., Vojtek, T., & Hutař, P. (2019). Finite element analysis of crack-tip opening displacement and plastic zones considering the cyclic material behaviour. Procedia Structural Integrity, 23, 529–534. https://doi.org/10.1016/j.prostr.2020.01.140

Tracey, D. M. (1971). Finite elements for determination of crack tip elastic stress intensity factors. Engineering Fracture Mechanics, 3(3), 255–265. https://doi.org/10.1016/0013-7944(71)90036-1

Wang, W., Kai, L., Gu, R., & Asundi, A. (2011). Dynamic Stress Concentration – a Hybrid Analysis. International Conference on Optics in Precision Engineering and Nanotechnology (ICOPEN 2011), 19, 220–226. https://doi.org/10.1016/j.phpro.2011.06.152

Wang, Y., Oyen, D., Guo, W., Mehta, A., Scott, C. B., Panda, N., Fernández-Godino, M. G., Srinivasan, G., & Yue, X. (2021). StressNet: Deep learning to predict stress with fracture propagation in brittle materials. npj Materials Degradation, 5, Article 6. https://doi.org/10.1038/s41529-021-00151-y

Zhang, J., He, X. D., Suo, B., & Du, S. Y. (2008). Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate. Engineering Fracture Mechanics, 75(18), 5217–5228. https://doi.org/10.1016/j.engfracmech.2008.08.006

Zhang, J.-Z., & Zhou, X.-P. (2020a). AE event rate characteristics of flawed granite: From damage stress to ultimate failure. Geophysical Journal International, 222(2), 795–814. https://doi.org/10.1093/gji/ggaa207

Zhang, J.-Z., & Zhou, X.-P. (2020b). Forecasting catastrophic rupture in brittle rocks using precursory AE time series. Journal of Geophysical Research: Solid Earth, 125, e2019JB019276. https://doi.org/10.1029/2019JB019276

Zhang, J.-Z., & Zhou, X.-P. (2022). Fracture process zone (FPZ) in quasi-brittle materials: Review and new insights from flawed granite subjected to uniaxial stress. Engineering Fracture Mechanics, 274, 108795. https://doi.org/10.1016/j.engfracmech.2022.108795

Zhang, J.-Z., Long, Y.-D., Zhang, T., & Zhou, X.-P. (2024). A true triaxial experiment investigation of the mechanical and deformation failure behaviours of flawed granite after exposure to high-temperature treatment. Engineering Fracture Mechanics, 306, 110273. https://doi.org/10.1016/j.engfracmech.2024.110273

Zhang, J.-Z., Zhou, X.-P., & Du, Y.-H. (2023). Cracking behaviours and acoustic emission characteristics in brittle failure of flawed sandstone: A true triaxial experiment investigation. Rock Mechanics and Rock Engineering, 56, 167–182. https://doi.org/10.1007/s00603-022-03087-0

Zhou, X.-P., Bi, J., & Qian, Q.-H. (2015). Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws. Rock Mechanics and Rock Engineering, 48, 1097–1114. https://doi.org/10.1007/s00603-014-0627-4

Zhou, X.-P., & Zhang, J.-Z. (2021). Damage progression and acoustic emission in brittle failure of granite and sandstone. International Journal of Rock Mechanics and Mining Sciences, 143, 104789. https://doi.org/10.1016/j.ijrmms.2021.104789