断裂相场模型的三维自适应有限元方法

裘沙沙; 刘星泽; 宁文杰; 姚伟岸; 段庆林

doi:10.21656/1000-0887.440299

断裂相场模型的三维自适应有限元方法

doi: 10.21656/1000-0887.440299

1.
大连理工大学工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116024
2.
大连理工大学大连理工大学白俄罗斯国立大学联合学院，辽宁大连 116024

基金项目:

中央高校基本科研业务费 DUT21GF304

详细信息

作者简介:
裘沙沙(1990—)，女，博士生(E-mail: 1065955826@qq.com)

通讯作者:
段庆林(1979—)，男，副教授，博士，博士生导师(通讯作者. E-mail: qinglinduan@dlut.edu.cn)

中图分类号: O302
计量
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- HTML全文浏览量: 135
- PDF下载量: 74
- 被引次数: 0
出版历程
- 收稿日期: 2023-10-03
- 修回日期: 2024-03-14
- 刊出日期: 2024-04-01

A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture

1.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China
2.
DUT-BSU Joint Institute, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

摘要

摘要: 发展了鲁棒的预测-校正算法，建立了断裂相场模型的三维自适应有限元分析.相场模型可以方便地处理复杂的断裂问题，避免了额外追踪裂纹路径且没有网格依赖性.然而，三维相场建模往往需要非常精细的网格，这降低了求解效率.针对该问题，基于交错求解方案发展了预测-校正网格自适应细化算法，实现了三维结构裂纹扩展的高精度分析.数值算例表明，所发展的方法能够准确合理地描述结构的裂纹扩展，同时网格可以在裂纹扩展的路径上自适应地细化.
- 断裂力学 /
- 相场模型 /
- 自适应细化 /
- 有限元法 /
- 三维裂纹
Abstract: A robust predictor-corrector algorithm was developed and a 3D adaptive finite element analysis for the fracture phase-field model was established. This model can deal with complex fracture problems conveniently, avoiding extra tracking of crack paths and without mesh-dependency. However, the 3D phase-field modeling usually requires extremely fine meshes, which brings reduction of the solving efficiency. Aimed at this problem, the predictor-corrector adaptive mesh refinement algorithm was developed based on a staggered solution scheme, to achieve high-precision analysis of crack propagation in 3D structures. Numerical examples show that, the developed method can accurately and reasonably describe crack propagation in structures, and the meshes can be adaptively refined along the crack propagation paths.
- fracture mechanics /
- phase-field model /
- adaptive refinement /
- finite element method /
- 3D crack

HTML全文

图 1 自适应网格细化示意图

Figure 1. Schematic diagram of the adaptive mesh refinement

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图 2 预测-校正算法

Figure 2. The predictor-corrector algorithm

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图 3 单槽方板拉伸

Figure 3. Tension of the single groove square plate

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图 4 单槽方板拉伸的网格比较

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. Meshes comparison for tension of the single groove square plate

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图 5 单槽带孔平板拉伸

Figure 5. Tension of the single groove plate with a hole

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图 6 双槽方板拉伸

Figure 6. Tension of the double groove square plate

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图 7 不同细化等级的断裂相场和自适应网格

Figure 7. The fracture phase field and adaptive meshes with different refinement levels

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图 8 r_max=3时的断裂相场

Figure 8. The fracture phase field for r_max=3

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图 9 r_max=3时的自适应网格和裂纹样式

Figure 9. Adaptive meshes and crack patterns for r_max=3

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表 1 单槽方板拉伸的节点数量、网格数量和CPU时间比较

Table 1. Comparison of node number, mesh number, and CPU time for tension of the single groove square plate

	node number	mesh number	CPU time t/min
preformed local refinement meshes	21 852	17 775	438
adaptive initial state adaptive final state	4 206 12 148	2 624 8 756	55

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参考文献(15)

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