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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (3): 573-582    DOI: 10.3785/j.issn.1008-973X.2023.03.015
土木工程     
基于强度理论的内聚力模型的有限元实现及应用
石天翔1(),张昕1,王洋洋1,郑克洪2,张永强1,*()
1. 浙江大学 建筑工程学院，浙江 杭州 310058
2. 浙江理工大学 机械工程学院，浙江 杭州 310018
Finite element implementation and application of strength theory based cohesive zone model
Tian-xiang SHI1(),Xin ZHANG1,Yang-yang WANG1,Ke-hong ZHENG2,Yong-qiang ZHANG1,*()
1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. School of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
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摘要：

在对基于强度理论的内聚力模型(ST-CZM)进行二维整理及三维拓展的基础上，使用Abaqus用户单元子程序(UEL)对该模型进行有限元实现. 通过经典界面破坏算例验证ST-CZM有限元模型的有效性和准确性，建立纤维增强复合材料(FRP)加固混凝土模型，采用ST-CZM模拟FRP与混凝土界面间的黏结破坏过程，实现ST-CZM在复杂工况下的应用. 相较于传统基于牵引力准则的内聚力模型，ST-CZM具有更灵活的混合模态耦合方式，且其切向和法向的强度模型相互独立，ST-CZM的收敛性更好，对强度的预测更准确. 所有算例表明，相较于传统基于牵引力准则的内聚力模型，ST-CZM有限元模型能够更好地实现黏结界面峰值应力的预测和损伤阶段的模拟.
关键词： 强度理论;  内聚力模型;  Abaqus UEL;  界面破坏    
Abstract:

The two-dimensional strength theory based cohesive zone model (ST-CZM) was extended to the three-dimensional case for a wider application. Furthermore, the finite element implementation of the ST-CZM was carried out using the Abaqus user element subroutine (UEL). The validity and accuracy of the ST-CZM were validated by several typical numerical benchmarks. On this basis, the ST-CZM finite element model was used to simulate the bond-slip behavior of the interface between fiber reinforced polymer (FRP) and concrete, which extended the application of the ST-CZM in complex working conditions. Compared to the traditional “traction laws” based cohesive zone model (CZM), the ST-CZM provides improved flexibility in mode mixity and allows independent selection of strength models in normal and tangent directions. In addition, the ST-CZM exhibits better convergence performance and more accurate strength predictions compared to “traction laws” based CZMs. All examples show that compared to the traditional “traction laws” based CZM, the ST-CZM finite element model can better predict the peak stress of the bonding interface and simulate the mixed-mode damage process, showing more realistic cracking process.
Key words: strength theory    cohesive zone model    Abaqus UEL    interface fracture
收稿日期: 2022-03-29 出版日期: 2023-03-31
CLC:  TB 121  
基金资助: 国家自然科学基金资助项目(12172019, 52004245)
通讯作者: 张永强     E-mail: stxzj@zju.edu.cn;cyqzhang@zju.edu.cn
作者简介: 石天翔 （1997—），男，硕士生，从事强度理论及断裂力学研究. orcid.org/0000-0001-6300-4138. E-mail： stxzj@zju.edu.cn
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引用本文:

石天翔,张昕,王洋洋,郑克洪,张永强. 基于强度理论的内聚力模型的有限元实现及应用[J]. 浙江大学学报(工学版), 2023, 57(3): 573-582.

Tian-xiang SHI,Xin ZHANG,Yang-yang WANG,Ke-hong ZHENG,Yong-qiang ZHANG. Finite element implementation and application of strength theory based cohesive zone model. Journal of ZheJiang University (Engineering Science), 2023, 57(3): 573-582.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.03.015    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I3/573

图 1  单向荷载下黏结单元应力-相对位移关系
图 2  二维牵引力破坏面
图 3  三维牵引力破坏面
模型 σI /MPa ueI/mm KI /(N·mm?3) GI/(N·mm?1) σII /MPa ueII /mm KII /(N·mm?3) GII /(N·mm?1)
双悬臂梁 30 3.0×10?4 1.0×105 0.26 60 6.0×10?4 1.0×105 1.002
固定比率混合 30 3.0×10?4 1.0×105 0.26 60 6.0×10?4 1.0×105 1.002
混合模态弯曲 100 4.0×10?4 2.5×105 0.50 100 4.0×10?4 2.5×105 0.500
表 1  基于强度理论的内聚力模型验证算例黏结单元参数[18]
模型 E11 /GPa E22, E33 /GPa G12, G13 /(N·mm?1) G23 /(N·mm?1) v12, v13 v23
双悬臂梁 120 10.5 5.25 3.48 0.30 0.51
固定比率混合 120 10.5 5.25 3.48 0.30 0.51
混合模态弯曲 122 122.0 — — 0.25 0.25
表 2  基于强度理论的内聚力模型验证算例的基体参数
图 4  双悬臂梁模型试样的几何尺寸及边界条件
图 5  双悬臂梁模型试验结果与数值模拟结果对比
图 6  固定比率混合模型边界条件
图 7  固定比率混合模型数值模拟结果对比
图 8  混合模态弯曲模型试样的几何尺寸
图 9  混合模态弯曲模型数值与解析结果对比
试验数值模型 σI /MPa ueI/mm KI /（N·mm?3） GI/（N·mm?1） σII /MPa ueII /mm KII /（N·mm?3） GII /（N·mm?1）
单剪 8.77 0.019 1 459.160 0.494 8.77 0.019 1 459.160 0.494
四点弯曲梁 12.00 0.029 0 0.297 0.891 12.00 0.029 0 0.297 0.891
表 3  基于强度理论内聚力模型实用算例黏结单元参数
图 10  单剪模型试件几何视图
图 11  单剪模型试验与数值模拟结果对比
图 12  单剪模型模拟过程损伤云图
图 13  四点弯曲梁模型几何视图
图 14  L2D1250试验裂缝图[24]
图 15  L2D1250局部脱黏标记图[24]
图 16  L2D1250模拟损伤云图
图 17  L2D1250试验与数值模拟结果对比
图 18  L2D1750试验裂缝图[24]
图 19  L2D1750局部脱黏标记图[24]
图 20  L2D1750模拟损伤云图
图 21  L2D1750试验与数值模拟结果对比
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