Page 167 - 《爆炸与冲击》2026年第5期

第 46 卷 第 5 期 爆 炸 与 冲 击 Vol. 46, No. 5
2026 年 5 月 EXPLOSION AND SHOCK WAVES May, 2026

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 *

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怯亚东 ，李 想 ，姚松林 ，张 豪 2
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（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）

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、几何和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、几何变动和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。
关键词： 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
中图分类号： O347 国标学科代码： 13015 文献标志码： A

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

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QIE Yadong , LI Xiang , YAO Songlin , ZHANG Hao 2
（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）

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

* 收稿日期： 2025-10-15；修回日期： 2026-03-31
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）
第一作者： 怯亚东（2001－ ），男，硕士，1027638952@qq.com
通信作者： 张 豪（1988－ ），男，博士，副研究员，haozhang@caep.cn

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