基于相场法与傅里叶神经算子的柱壳裂纹演化预测方法

怯亚东; 李想; 姚松林; 张豪

doi:10.11883/bzycj-2025-0343

基于相场法与傅里叶神经算子的柱壳裂纹演化预测方法

doi: 10.11883/bzycj-2025-0343

怯亚东^1,,
李想¹,
姚松林²,
张豪^2, ,

1.
海南师范大学信息科学技术学院，海南海口 570100
2.
中国工程物理研究院流体物理研究所冲击波物理与爆轰物理全国重点实验室，四川绵阳 621999

基金项目: 国家自然科学基金（12162012，12141203）；中国工程物理研究院院长基金（YZJJZQ2023001）；冲击波物理与爆轰物理全国重点实验室基金（2023JCJQLB05408）

详细信息

作者简介:
怯亚东（2001－　），男，硕士，1027638952@qq.com

通讯作者:
张　豪（1988－　），男，博士，副研究员，haozhang@caep.cn

中图分类号: O347
计量
- 文章访问数: 24
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- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2025-10-15
- 修回日期: 2026-03-31
- 网络出版日期: 2026-04-16

A phase-field and Fourier neural operator-based method for predicting crack evolution in column-shell structures

1.
School of Information Science and Technology, Hainan Normal University, Haikou 570100, Hainan, China
2.
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China

摘要

摘要: 为应对传统有限元模拟柱壳结构断裂行为时计算成本高昂的挑战，提出了一种结合相场法与傅里叶神经算子（Fourier neural operator, FNO）的柱壳裂纹演化预测框架。相场法能够自然捕捉裂纹的萌生、扩展与愈合过程，而FNO模型则通过学习临界能量释放率分布、几何与载荷条件与裂纹演化之间的映射关系，实现对裂纹全过程的高效预测。首先，建立了基于有限元的柱壳相场模型，生成裂纹演化数据；随后，构建并训练了用于裂纹萌生与扩展的串联FNO框架。结果表明，该方法不仅在随机临界能量释放率、几何变动与复杂载荷条件下保持了较高的预测精度，而且在计算效率上显著优于传统有限元模拟。
- 柱壳结构 /
- 相场法 /
- 傅里叶神经算子 /
- 裂纹萌生与扩展 /
- 数据驱动
Abstract: With the increasing application of engineering structures under extreme conditions, accurately predicting their fracture behavior has become a critical challenge in materials science and fracture mechanics. Column-shell structures, as typical load-bearing components, are highly sensitive to crack initiation and propagation, which directly affect their safety and reliability. Although traditional finite element methods can provide accurate fracture evolution simulations, their high computational cost limits applicability in rapid prediction scenarios.To address this issue, a hybrid framework that integrates the phase-field method with the Fourier neural operator (FNO) is proposed for predicting the fracture evolution of column-shell structures. In the proposed framework, the phase-field method is first employed to describe crack initiation, propagation, and possible coalescence in a continuous manner, avoiding explicit crack tracking and enabling physically consistent simulations. Based on this formulation, a finite element model of the column-shell structure is established to generate high-fidelity fracture evolution data under various conditions, including different critical energy release rates, geometric configurations, and loading scenarios.Subsequently, a data-driven learning framework is developed using the FNO to approximate the nonlinear mapping between input parameters and fracture responses. The input of the model includes the spatial distribution of the critical energy release rate, geometric features, and applied loading conditions, while the output corresponds to the evolving phase-field variable that characterizes crack growth over time. A series of FNO models are constructed and trained in a sequential manner to separately capture crack initiation and propagation stages, forming a coupled prediction framework. The training process is carried out using the generated dataset, with appropriate normalization and validation strategies to ensure model robustness and generalization capability.The results demonstrate that the proposed method achieves high prediction accuracy under random critical energy release rates, varying geometries, and complex loading conditions, while significantly reducing computational cost compared to conventional finite element simulations. Once trained, the model enables near real-time prediction of fracture evolution.
- column-shell structure /
- phase-field method /
- Fourier neural operator /
- crack initiation and propagation /
- data-driven

HTML全文

图 1 傅里叶神经算子模型的结构示意图

Figure 1. Architecture of the Fourier neural operator (FNO) model

下载: 全尺寸图片幻灯片

图 2 基于Abaqus的柱壳裂纹演化的有限元模型计算过程示意图

Figure 2. Schematic diagram of the calculation process for the finite element model of crack evolution in cylindrical shells based on Abaqus

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图 3 两个模型的训练和测试误差随迭代轮数的收敛曲线

Figure 3. Convergence curves of training and testing errors of the two models with respect to iteration number

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图 4 随机分布能量释放率条件下的相场预测结果与真实结果的对比

Figure 4. Comparison of phase field prediction results and actual results under the condition of randomly distributed energy release rate

下载: 全尺寸图片幻灯片

图 5 随机分布临界能量释放率与变几何条件下的相场预测结果与真实结果的对比

Figure 5. Comparison of phase field prediction results and actual results under conditions of randomly distributed critical energy release rate and variable geometry

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图 6 随机分布临界能量释放率与变载荷条件下的相场预测结果与真实结果的对比

Figure 6. Comparison of phase field prediction results and actual results under conditions of randomly distributed critical energy release rate and variable load

下载: 全尺寸图片幻灯片

表 1 模型1的结构

Table 1. Structure of model 1

层编号	方程	卷积核	步长	填充	输出形状
输入					2×100×863×15
1	Fc0	1	1	38	2×100×863×38
2	Permute				2×38×100×863
3	Fourier layer 1				2×38×100×863
4	Fourier layer 2				2×38×100×863
5	Fourier layer 3				2×38×100×863
6	Fourier layer 4				2×38×100×863
7	Conv3d	1	1	0	2×38×100×863
7	ReLU				2×38×100×863
8	Conv3d	1	1	0	2×38×100×863
8	ReLU				2×38×100×863
9	Conv3d	1	1	0	2×38×100×863
9	ReLU				2×38×100×863
10	Permute				2×100×863×38
11	Fc1				2×100×863×8
12	GELU				2×100×863×8
13	Fc2				2×100×863×1
14	View				2×100×863×1

下载: 导出CSV

表 2 模型2的结构

Table 2. Structure of model 2

层编号	方程	卷积核	步长	填充	输出形状
输入					2×100×863×15
1	Fc0	1	1	38	2×100×863×38
2	Permute				2×38×100×863
3	Fourier layer 1				2×38×100×863
4	Fourier layer 2				2×38×100×863
5	Fourier layer 3				2×38×100×863
6	Fourier layer 4				2×38×100×863
7	Conv3d	1	1	0	2×38×100×863
7	ReLU				2×38×100×863
8	Conv3d	1	1	0	2×38×100×863
8	ReLU				2×38×100×863
9	Conv3d	1	1	0	2×38×100×863
9	ReLU				2×38×100×863
10	Permute				2×100×863×38
11	Fc1				2×100×863×8
12	GELU				2×100×863×8
13	Fc2				2×100×863×1
14	View				2×100×863×1

下载: 导出CSV

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