Cracks in crystalline silicon photovoltaic (PV) cells are a major reliability concern, because they reduce power output and shorten module service life. Numerical modeling has become an effective approach for understanding crack initiation and propagation under various manufacturing and operating conditions. This review presents recent advances in the application of the Finite Element Method (FEM) and the Extended Finite Element Method (XFEM) for modeling cracks in crystalline silicon photovoltaic cells. Following the PRISMA methodology, studies published between 2021 and 2026 were systematically reviewed to examine crack formation mechanisms, FEM and XFEM modeling approaches, material assumptions, loading conditions, and key findings. The review shows that FEM is widely employed to predict stress distribution, deformation, and thermo-mechanical behavior during manufacturing, transportation, installation, and service, while XFEM effectively simulates crack initiation and propagation without the need for remeshing. The reviewed studies further demonstrate that manufacturing-induced residual stresses, thermal cycling, mechanical loading, wafer thickness, and crack orientation significantly influence crack evolution and module reliability. However, several limitations remain, including simplified material assumptions, isolated treatment of loading conditions, limited consideration of electrical degradation, and insufficient experimental validation under realistic operating environments. The review highlights these challenges and identifies future research needs toward more comprehensive and experimentally validated numerical models capable of accurately predicting both crack evolution and the long-term reliability of crystalline silicon photovoltaic modules.
References
[1]
Atta, S., Kerubo, M.L., Sabisa, N.E., Adu-Gyamfi, D., Appiah, S.A. and Onyishi, E.E. (2025) Environmental Corrosion and Long-Term Degradation of Crystalline Silicon Solar Cells: Mechanisms, Climate Effects and Mitigation Strategies. Current Journal of Applied Science and Technology, 44, 9-18. https://doi.org/10.9734/cjast/2025/v44i104616
[2]
Papargyri, L., Theristis, M., Kubicek, B., Krametz, T., Mayr, C., Papanastasiou, P., et al. (2020) Modelling and Experimental Investigations of Microcracks in Crystalline Silicon Photovoltaics: A Review. Renewable Energy, 145, 2387-2408. https://doi.org/10.1016/j.renene.2019.07.138
[3]
Du, Y., Dai, J., Xin, S., Ma, K., Zhang, M., Li, T., et al. (2025) Thermo-Mechanical Stress Modelling and Fracture Analysis on Ultra-Thin Silicon Solar Cell Based on Super Multi-Busbar PV Modules. Engineering Failure Analysis, 169, Article ID: 109153. https://doi.org/10.1016/j.engfailanal.2024.109153
[4]
M., M., Gembali, M., Narayanan, K.R. and K., J. (2021) Analysis of Micro-Cracks Evolution in Silicon Cell during Entire Solar Photovoltaic Module Manufacturing Process. Solar Energy, 224, 1160-1169. https://doi.org/10.1016/j.solener.2021.06.075
[5]
Papargyri, L., Papanastasiou, P. and Georghiou, G.E. (2024) Sequential Thermomechanical Stress and Cracking Analysis of Photovoltaic Modules with Full and Half-Cut Cells. Solar Energy Materials and Solar Cells, 278, Article ID: 113166. https://doi.org/10.1016/j.solmat.2024.113166
[6]
Jiao, B., Fang, Q., Liu, C., Zhang, Y., Shen, Y., Shen, Y., et al. (2026) Numerical Investigation of Crack Propagation in PV Modules with Initial Micro-Cracks. Solar Energy Materials and Solar Cells, 297, Article ID: 114120. https://doi.org/10.1016/j.solmat.2025.114120
[7]
K？ntges, M., Siebert, M., Morlier, A., Illing, R., Bessing, N. and Wegert, F. (2016) Impact of Transportation on Silicon Wafer-Based Photovoltaic Modules. Progress in Photovoltaics: Research and Applications, 24, 1085-1095. https://doi.org/10.1002/pip.2768
[8]
Desai, U., Vasudevan, D.P., Kottantharayil, A. and Singh, A. (2021) Prediction of Vibration Induced Damage in Photovoltaic Modules during Transportation: Finite Element Model and Field Study. Engineering Research Express, 3, Article ID: 045045. https://doi.org/10.1088/2631-8695/ac3d12
[9]
Ngenzi, A., Akinlabi, S.A. and Muchiri, A.K. (2023) Predicting the Volume Fraction of Martensite in Welded Mild Steel Joint Reinforced with Titanium Alloy Powder. Modeling and Numerical Simulation of Material Science, 13, 11-27. https://doi.org/10.4236/mnsms.2023.132002
[10]
Ngenzi, A. (2026) Modeling Ferrite Formation in Mild Steel Weld Using FEM and JMAK Equation. International Journal of Innovative Science and Research Technology, 11, 3628-3636. https://doi.org/10.38124/ijisrt/26jan1428
[11]
Wang, Z., Hsiao, P., Song, N., Shen, X., Xu, C., Yi, H., et al. (2023) Use Finite Element Modelling to Characterise the Stress Evolution in Multi Busbar Interconnected Half-Cell Tiled Modules after Soldering and Lamination. Solar Energy Materials and Solar Cells, 252, Article ID: 112166. https://doi.org/10.1016/j.solmat.2022.112166
[12]
Papargyri, L., Papanastasiou, P. and Georghiou, G.E. (2022) Effect of Materials and Design on PV Cracking under Mechanical Loading. Renewable Energy, 199, 433-444. https://doi.org/10.1016/j.renene.2022.09.009
[13]
Beroual, S., Hrairi, M., Yatim, N.M. and Dawood, M.S.I. (2023) Solar Cell Micro Crack Detection Technique Using Electromechanical Impedance and Finite Element Analysis. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 238, 3531-3548. https://doi.org/10.1177/09544062231198776
[14]
Roy, S., Baruah, M.S., Sahu, S. and Nayak, B.B. (2021) Computational Analysis on the Thermal and Mechanical Properties of Thin Film Solar Cells. Materials Today: Proceedings, 44, 1207-1213. https://doi.org/10.1016/j.matpr.2020.11.241
[15]
Tariq, M., Safdar, N., Scheffler, S. and Rolfes, R. (2022) Numerical Homogenization of Poly-Crystalline Silicon Wafer Based Photovoltaic Modules Including Pre-Cracks. Materials Today Communications, 33, Article ID: 104752. https://doi.org/10.1016/j.mtcomm.2022.104752
[16]
Halkiopoulos, C. and Gkintoni, E. (2024) Leveraging AI in E-Learning: Personalized Learning and Adaptive Assessment through Cognitive Neuropsychology—A Systematic Analysis. Electronics, 13, Article 3762. https://doi.org/10.3390/electronics13183762
[17]
Budiman, A.S., Anbazhagan, S., Illya, G., Song, W.J.R., Sahay, R., Tippabhotla, S.K., et al. (2021) Enabling Curvable Silicon Photovoltaics Technology Using Polycarbonate-Sandwiched Laminate Design. Solar Energy, 220, 462-472. https://doi.org/10.1016/j.solener.2021.03.021
[18]
Infuso, A., Corrado, M. and Paggi, M. (2014) Image Analysis of Polycrystalline Solar Cells and Modelling of Intergranular and Transgranular Cracking. Journal of the European Ceramic Society, 34, 2713-2722. https://doi.org/10.1016/j.jeurceramsoc.2013.12.051
[19]
Rupnowski, P. and Sopori, B. (2009) Strength of Silicon Wafers: Fracture Mechanics Approach. International Journal of Fracture, 155, 67-74. https://doi.org/10.1007/s10704-009-9324-9
[20]
Ennemri, A., Logerais, P.O., Balistrou, M., Durastanti, J., Belaidi, I., et al. (2019) Cracks in Silicon Photovoltaic Modules: A Review. Journal of Optoelectronics and Advanced Materials, 21, 74-92. https://www.researchgate.net/publication/331502743_Cracks_in_silicon_photovoltaic_modules_a_review
[21]
Kajari-Schr？der, S., Kunze, I., Eitner, U. and K？ntges, M. (2011) Spatial and Orientational Distribution of Cracks in Crystalline Photovoltaic Modules Generated by Mechanical Load Tests. Solar Energy Materials and Solar Cells, 95, 3054-3059. https://doi.org/10.1016/j.solmat.2011.06.032
[22]
Zarmai, M.T., Ekere, N.N., Oduoza, C.F. and Amalu, E.H. (2017) Evaluation of Thermo-Mechanical Damage and Fatigue Life of Solar Cell Solder Interconnections. Robotics and Computer-Integrated Manufacturing, 47, 37-43. https://doi.org/10.1016/j.rcim.2016.12.008
[23]
Tao, W.S., Bao, G.C., Liu, J.H., Zhang, M., Wang, L.C., Dai, J., et al. (2022) Modeling and Experimental Investigations of Thermo-Mechanical Stress Induced Micro-Cracks in Different Crystalline Silicon Photovoltaic Modules. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4046698
[24]
Vasudevan, D.P., Bhatt, P. and Kottantharayil, A. (2020) Lateral Vibrations Experienced by Vertically Placed PV Modules in the Pallet during Transportation. 2020 47th IEEE Photovoltaic Specialists Conference (PVSC), Calgary, 15 June-21 August 2020, 1323-1325. https://doi.org/10.1109/pvsc45281.2020.9301001
[25]
Ma, S., Yuan, G., Zhang, Y., Yang, N., Li, Y. and Chen, Q. (2022) Development of Encapsulation Strategies towards the Commercialization of Perovskite Solar Cells. Energy & Environmental Science, 15, 13-55. https://doi.org/10.1039/d1ee02882k
[26]
Wakchaure, M.B., Misra, M. and Menezes, P.L. (2024) A Comprehensive Review on Finite Element Analysis of Laser Shock Peening. Materials, 17, Article 4174. https://doi.org/10.3390/ma17174174
[27]
Sato, D., Kobayashi, H., Masuda, T., Araki, K., Miyashita, Y. and Yamada, N. (2025) Structural Design and Demonstration of Three-Dimensional Curved Photovoltaic Modules Using Crystalline Silicon Solar Cells. Solar Energy Materials and Solar Cells, 279, Article ID: 113258. https://doi.org/10.1016/j.solmat.2024.113258
[28]
Bhore, C.V., Andhare, A.B., Padole, P.M., Loyte, A., Sofia Vincent, J., Devarajan, Y., et al. (2023) Experimental Investigation on Minimizing Degradation of Solar Energy Generation for Photovoltaic Module by Modified Damping Systems. Solar Energy, 250, 194-208. https://doi.org/10.1016/j.solener.2022.12.015
[29]
Al Ahmar, J. and Wiese, S. (2014) A Crack Analysis Model for Silicon Based Solar Cells. 2014 15th International Conference on Thermal, Mechanical and Mulit-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), Ghent, 7-9 April 2014, 1-5. https://doi.org/10.1109/eurosime.2014.6813855
[30]
Wang, Z. (2025) Thermomechanical Stress in Solar Cells and Modules: A Finite Element Modelling and Experimental Investigation. Ph.D. Thesis, UNSW Sydney. https://doi.org/10.26190/unsworks/31896
[31]
Zhang, Q.Z., Shu, B.F., Chen, M.B., Liang, Q.B., Fan, C., Feng, Z.Q., et al. (2015) Numerical Investigation on Residual Stress in Photovoltaic Laminates after Lamination. Journal of Mechanical Science and Technology, 29, 655-662. https://doi.org/10.1007/s12206-015-0125-y
[32]
Sposato, A., Martino, G.D., Stigliano, G., Cignali, C., Dassisti, M. and Umbrello, D. (2026) Numerical Modelling of Delamination of Crystalline Photovoltaic Modules to Enable Efficient Recycling. Procedia Computer Science, 277, 473-483. https://doi.org/10.1016/j.procs.2026.02.089
[33]
Lu, Y., Wang, Z. and Chong, K. (2005) A Comparative Study of Buried Structure in Soil Subjected to Blast Load Using 2D and 3D Numerical Simulations. Soil Dynamics and Earthquake Engineering, 25, 275-288. https://doi.org/10.1016/j.soildyn.2005.02.007
[34]
Zhang, Y., Liu, Q., Hou, J., Ni, Y., Yu, Y., Jaubert, J., et al. (2021) Experimental Study on Micro-Crack Initiation in Photovoltaic Polycrystalline Silicon Wafer. Materials Science in Semiconductor Processing, 123, Article ID: 105539. https://doi.org/10.1016/j.mssp.2020.105539
[35]
Cheng, D. and Gao, Y. (2022) Finite Element Analysis of the Clamping Stress of Photovoltaic Silicon Brick in Diamond Wire Sawing. Materials Science in Semiconductor Processing, 147, Article ID: 106732. https://doi.org/10.1016/j.mssp.2022.106732
[36]
Vellwock, A.E. and Libonati, F. (2024) XFEM for Composites, Biological, and Bioinspired Materials: A Review. Materials, 17, Article 745. https://doi.org/10.3390/ma17030745
[37]
Raj, V.R., Priya, R.K., Bindu, K.V., Prabhu, N., Madhavarao, S., Ramkumar, G., et al. (2022) Demonstrating and Investigating the Mechanical Strength of Solar Cells. International Journal of Photoenergy, 2022, Article ID: 4713869. https://doi.org/10.1155/2022/4713869
[38]
Nikitin, S.E., Shpeizman, V.V., Pozdnyakov, A.O., Stepanov, S.I., Timashov, R.B., Nikolaev, V.I., et al. (2022) Fracture Strength of Silicon Solar Wafers with Different Surface Textures. Materials Science in Semiconductor Processing, 140, Article ID: 106386. https://doi.org/10.1016/j.mssp.2021.106386
[39]
Kumar Laha, S., Kumar Sadhu, P., Ganguly, A. and Kumar Naskar, A. (2022) A Comparative Study on Thermal Performance of a 3-D Model Based Solar Photovoltaic Panel through Finite Element Analysis. Ain Shams Engineering Journal, 13, Article ID: 101533. https://doi.org/10.1016/j.asej.2021.06.019
[40]
Klasen, N., Heinz, F., De Rose, A., Roessler, T., Kraft, A. and Kamlah, M. (2022) Root Cause Analysis of Solar Cell Cracks at Shingle Joints. Solar Energy Materials and Solar Cells, 238, Article ID: 111590. https://doi.org/10.1016/j.solmat.2022.111590
[41]
Fang, Q., Jiao, B., Yu, D., Liu, C. and Liu, P. (2026) Investigation of Fatigue Crack Propagation in Photovoltaic Modules under Dynamic Cyclic Loading. Solar Energy, 304, Article ID: 114217. https://doi.org/10.1016/j.solener.2025.114217
