Page 178 - 《爆炸与冲击》2026年第5期

第 46 卷 怯亚东，等： 基于相场法与傅里叶神经算子的柱壳裂纹演化预测方法 第 5 期

[15] HANSEN-DÖRR A C, DE BORST R, HENNIG P, et al. Phase-field modelling of interface failure in brittle materials [J].
Computer Methods in Applied Mechanics and Engineering, 2019, 346: 25–42. DOI: 10.1016/j.cma.2018.11.020.
[16] WAMBACQ J, ULLOA J, LOMBAERT G, et al. Interior-point methods for the phase-field approach to brittle and ductile
fracture [J]. Computer Methods in Applied Mechanics and Engineering, 2021, 375: 113612. DOI: 10.1016/j.cma.2020.113612.
[17] GAO J, BAI Y L, HE X D, et al. A phase field and machining-learning approach for rapid and accurate prediction of
composites failure [J]. Journal of Reinforced Plastics and Composites, 2025, 44(13/14): 743–755. DOI: 10.1177/
07316844241228182.
[18] AMBATI M, GERASIMOV T, DE LORENZIS L. A review on phase-field models of brittle fracture and a new fast hybrid
formulation [J]. Computational Mechanics, 2015, 55(2): 383–405. DOI: 10.1007/s00466-014-1109-y.
[19] ZHANG X, VIGNOLLET J, MOËS N. A phase-field model for mixed-mode fracture [J]. Computer Methods in Applied
Mechanics and Engineering, 2018, 328: 471–493.
[20] NGUYEN T T, YVONNET J, ZHU Q Z, et al. A phase-field method for computational modeling of interfacial damage
interacting with crack propagation in realistic microstructures obtained by microtomography [J]. Computer Methods in
Applied Mechanics and Engineering, 2016, 312: 567–595. DOI: 10.1016/j.cma.2015.10.007.
[21] FARRELL P E, MAURINI C, BOURDIN B. Splitting schemes for phase-field fracture problems [J]. Journal of
Computational Physics, 2019, 375: 145–173.
[22] LI Z Y, KOVACHKI N B, AZIZZADENESHELI K, et al. Fourier neural operator for parametric partial differential
equations [C]//Proceedings of the 9th International Conference on Learning Representations. OpenReview. net, 2021.
[23] KOVACHKI N, LI Z Y, LIU B, et al. Neural operator: learning maps between function spaces with applications to PDEs [J].
The Journal of Machine Learning Research, 2023, 24(1): 89.
[24] JIANG P S, YANG Z, WANG J L, et al. Efficient super-resolution of near-surface climate modeling using the Fourier neural
operator [J]. Journal of Advances in Modeling Earth Systems, 2023, 15(7): e2023MS003800. DOI: 10.1029/2023MS003800.
[25] LI Z J, PENG W H, YUAN Z L, et al. Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural
operator [J]. Physics of Fluids, 2023, 35(7): 075145. DOI: 10.1063/5.0158830.
[26] YOU H Q, ZHANG Q, ROSS C J, et al. Learning deep implicit Fourier neural operators (IFNOs) with applications to
heterogeneous material modeling [J]. Computer Methods in Applied Mechanics and Engineering, 2022, 398: 115296. DOI:
10.1016/j.cma.2022.115296.
[27] ZHANG H, PEI X Y, PENG H, et al. Phase-field modeling of spontaneous shear bands in collapsing thick-walled cylinders [J].
Engineering Fracture Mechanics, 2021, 249: 107706. DOI: 10.1016/j.engfracmech.2021.107706.
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