A phase field - UEL framework for crack branching simulation in concrete
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/23425Keywords:
crack branching, crack propagation, phase field, UEL, ABAQUSAbstract
Crack branching significantly affects the fracture behavior of concrete, yet its modeling remains challenging due to the quasi-brittle nature of the material. This study presents an implementation of the Phase Field Method (PFM) within Abaqus using a User Element (UEL) subroutine to simulate the initiation and propagation of cracks in pre-notched concrete plates. The proposed framework enables a continuous description of fracture without explicit crack surface tracking, thus providing numerical stability when complex branching occurs. Through a series of simulations, the influence of material properties, loading configurations, and mesh resolution on crack evolution is examined. The findings demonstrate that the PFM--UEL framework can effectively capture branching patterns and deliver consistent fracture responses, thereby underscoring its potential as a robust tool for analyzing concrete failure and supporting future data-driven modeling efforts.
Downloads
References
Abdulridha Lateef, H., Mahmood Laftah, R., & Abdulrazzaq Jasim, N. (2022). Investigation of crack propagation in plain concrete using Phase-field model. Materials Today: Proceedings, 57, 375–382. https://doi.org/10.1016/j.matpr.2021.12.146
Anh, V. T. T., Dinh, T. H., Giang, V. D., Le, C. H., Dat, N. D., & Duc, N. D. (2025). Concrete crack simulation and its machine learning application in propagation prediction. Archives of Civil and Mechanical Engineering, 25(4). https://doi.org/10.1007/s43452-025-01229-z
Azinpour, E., Rzepa, S., Melzer, D., Reis, A., Džugan, J., & Cesar de Sa, J. M. A. (2023). Phase-field ductile fracture analysis of multi-materials and functionally graded composites through numerical and experimental methods. Theoretical and Applied Fracture Mechanics, 125, 103906. https://doi.org/10.1016/j.tafmec.2023.103906
Bažant, Z. P., & Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press. https://doi.org/10.1201/9780203756799
Borden, M. J., Verhoosel, C. V., Scott, M. A., Hughes, T. J. R., & Landis, C. M. (2012). A phase-field description of dynamic brittle fracture. Computer Methods in Applied Mechanics and Engineering, 217–220, 77–95. https://doi.org/10.1016/j.cma.2012.01.008
Chung, N. T., Hai, H., & Hee, S. S. (2016). Dynamic Analysis of High Building with Cracks in Column Subjected to Earthquake Loading. American Journal of Civil Engineering, 4(5), 233–240. https://doi.org/10.11648/j.ajce.20160405.14
Dinh, T. H., Anh, V. T. T., Nguyen, T., Hieu Le, C., Trung, N. L., Duc, N. D., & Lin, C.-T. (2023). Towards Vision-based Concrete Crack Detection: Automatic Simulation of Real-world Cracks. IEEE Transactions on Instrumentation and Measurement, 72, 1–15. https://doi.org/10.1109/tim.2023.3328076
Dorduncu, M., Ren, H., Zhuang, X., Silling, S., Madenci, E., & Rabczuk, T. (2024). A review of peridynamic theory and nonlocal operators along with their computer implementations. Computers & Structures, 299, 107395. https://doi.org/10.1016/j.compstruc.2024.107395
Duc, N. D., Duc, D. H., Thom, D. V., & Truong, T. D. (2018). A static buckling investigation of multi-cracked FGM plate based phase-field method coupling the new TSDT. Acta Mechanica. https://doi.org/10.1007/s00707-018-2256-6
Giannella, V., Bardozzo, F., Postiglione, A., Tagliaferri, R., Sepe, R., & Armentani, E. (2023). Neural networks for fatigue crack propagation predictions in real-time under uncertainty. Composite Structures, 288, 107157. https://doi.org/10.2139/ssrn.4347466
Hai, L., Zhang, H., Wriggers, P., Huang, Y. J., Zhuang, X. Y., & Xu, S. L. (2024). 3D concrete fracture simulations using an explicit phase field model. International Journal of Mechanical Sciences, 265, 108907. https://doi.org/10.1016/j.ijmecsci.2023.108907
Hang, P. T. (2015). Frequency spectrum method in the study of vibration of cracked elastic beams under moving loads [PhD Thesis]. Hanoi.
Huong, N. T. V. (2016). Bending vibration of prestressed beams under the action of moving bodies [PhD Thesis]. Hanoi.
Huong, N. T. V., Khang, N. V., & Dien, N. P. (2015). Dynamic response of a cracked and prestressed beam under the action of a moving body. Journal of Science and Technology (Technical Universities), 106, 58–62.
Jia, M., Wu, Z., Yu, R. C., & Zhang, X. (2022). Experimental investigation of mixed mode I–II fatigue crack propagation in concrete using a digital image correlation method. Engineering Fracture Mechanics, 272, 108712. https://doi.org/10.1016/j.engfracmech.2022.108712
Khan, G., Ahmed, A., Liu, Y., Tafsirojjaman, T., Ahmad, A., & Iqbal, M. (2023). Phase field model for mixed mode fracture in concrete. Engineering Fracture Mechanics, 289, 109439. https://doi.org/10.1016/j.engfracmech.2023.109439
Khiem, N., & Hang, P. (2017). Analysis and identification of multiple-cracked beam subjected to moving harmonic load. Journal of Vibration and Control, 24(13), 2782–2801. https://doi.org/10.1177/1077546317694496
Li, X., & Xu, Y. (2022). Phase field modeling scheme with mesostructure for crack propagation in concrete composite. International Journal of Solids and Structures, 234–235, 111259. https://doi.org/10.1016/j.ijsolstr.2021.111259
Miehe, C., Hofacker, M., & Welschinger, F. (2010). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45–48), 2765–2778. https://doi.org/10.1016/j.cma.2010.04.011
Minh, P. P., Van Do, T., Duc, D. H., & Duc, N. D. (2018). The stability of cracked rectangular plate with variable thickness using phase field method. Thin-Walled Structures, 129, 157–165. https://doi.org/10.1016/j.tws.2018.03.028
Molnár, G., Gravouil, A., Seghir, R., & Réthoré, J. (2020). An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation. Computer Methods in Applied Mechanics and Engineering, 365, 113004. https://doi.org/10.1016/j.cma.2020.113004
Nair, K. A., & Ghosh, S. (2023). Crack tip enhanced phase field model for crack evolution in crystalline Ti6Al from concurrent crystal plasticity FE-molecular dynamics simulations. European Journal of Mechanics - A/Solids, 100, 104983. https://doi.org/10.1016/j.euromechsol.2023.104983
Navidtehrani, Y., Betegón, C., & Martínez-Pañeda, E. (2021a). A simple and robust Abaqus implementation of the phase field fracture method. Applications in Engineering Science, 6, 100050. https://doi.org/10.1016/j.apples.2021.100050
Navidtehrani, Y., Betegón, C., & Martínez-Pañeda, E. (2021b). A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine. Materials, 14(8), 1913. https://doi.org/10.3390/ma14081913
Ožbolt, J., Bošnjak, J., & Sola, E. (2013). Dynamic fracture of concrete compact tension specimen: Experimental and numerical study. International Journal of Solids and Structures, 50(25–26), 4270–4278. https://doi.org/10.1016/j.ijsolstr.2013.08.030
Pham, K., Amor, H., Marigo, J. J., & Maurini, C. (2011). Gradient damage models and their use to approximate brittle fracture. International Journal of Damage Mechanics, 20(4), 618–652.
Reddy, S. S. K., Amirtham, R., & Reddy, J. N. (2021). Modeling fracture in brittle materials with inertia effects using the phase field method. Mechanics of Advanced Materials and Structures, 30(1), 144–159. https://doi.org/10.1080/15376494.2021.2010289
Sun, Y., Edwards, M. G., Chen, B., & Li, C. (2021). A state-of-the-art review of crack branching. Engineering Fracture Mechanics, 257, 108036. https://doi.org/10.1016/j.engfracmech.2021.108036
Tanné, E., Li, T., Bourdin, B., Marigo, J.-J., & Maurini, C. (2018). Crack nucleation in variational phase-field models of brittle fracture. Journal of the Mechanics and Physics of Solids, 110, 80–99. https://doi.org/10.1016/j.jmps.2017.09.006
Truong, T. T., Lo, V. S., Nguyen, M. N., Nguyen, N. T., & Nguyen, D. K. (2021). Evaluation of fracture parameters in cracked plates using an extended meshfree method. Engineering Fracture Mechanics, 247, 107671. https://doi.org/10.1016/j.engfracmech.2021.107671
Vedrtnam, A., Gunwant, D., Kalauni, K., & Palou, M. T. (2025). Experimental and numerical study on sustainable post-fire repair of concrete structures using bacterial self-healing mechanisms. Construction and Building Materials, 474, 141175. https://doi.org/10.1016/j.conbuildmat.2025.141175
Wang, C., Ping, X., & Wang, X. (2023). An adaptive finite element method for crack propagation based on a multifunctional super singular element. International Journal of Mechanical Sciences, 247, 108191. https://doi.org/10.1016/j.ijmecsci.2023.108191
Wang, L.-X., Wen, L.-F., Tian, R., & Feng, C. (2024). Improved XFEM (IXFEM): Arbitrary multiple crack initiation, propagation and interaction analysis. Computer Methods in Applied Mechanics and Engineering, 421, 116791. https://doi.org/10.1016/j.cma.2024.116791
Weng, X., Huang, Y., & Wang, W. (2019). Segment-based pavement crack quantification. Automation in Construction, 105, 102819. https://doi.org/10.1016/j.autcon.2019.04.014
Wu, J.-Y., & Nguyen, V. P. (2018). A length scale insensitive phase-field damage model for brittle fracture. Journal of the Mechanics and Physics of Solids, 119, 20–42. https://doi.org/10.1016/j.jmps.2018.06.006
Yin, Y., Qiao, Y., & Hu, S. (2019). Four-point bending tests for the fracture properties of concrete. Engineering Fracture Mechanics, 211, 371–381. https://doi.org/10.1016/j.engfracmech.2019.03.004
Yu, X., Wang, R., Dong, C., Ji, J., & Zhen, X. (2023). 3D implementation of push-out test in ABAQUS using the phase-field method. Journal of Mechanical Science and Technology, 37(4), 1731–1745. https://doi.org/10.1007/s12206-023-0314-z
Zhang, P., Cui, Y., Douglas, K., Song, C., & Russell, A. R. (2025). Phase field fracture modeling of cohesive-frictional materials like concrete and rock using the scaled boundary finite element method. Computers and Geotechnics, 180, 107106. https://doi.org/10.1016/j.compgeo.2025.107106
Zhou, C., Hu, M., Xie, D., Wang, Y., & He, J. (2023). Finite element-based phase field simulation of complex branching crack propagation under different loads. Mechanics of Advanced Materials and Structures, 31(18), 4269–4279. https://doi.org/10.1080/15376494.2023.2193184
Downloads
Published
How to Cite
License

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



