模拟动断裂问题的多尺度扩展有限元方法

张凝; 尹硕辉; 赵子衡

doi:10.13433/j.cnki.1003-8728.20200429

模拟动断裂问题的多尺度扩展有限元方法

doi: 10.13433/j.cnki.1003-8728.20200429

湘潭大学机械工程学院, 湖南湘潭 411105

详细信息

作者简介:
张凝(1996-), 硕士研究生, 研究方向为结构断裂数值仿真, 1049295559@qq.com

通讯作者:
尹硕辉, 副教授, 博士, yinsh2016@163.com

中图分类号: O346.1
计量
- 文章访问数: 93
- HTML全文浏览量: 48
- PDF下载量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2020-10-20
- 刊出日期: 2022-05-01

Multi-scale XFEM for Simulating Dynamic Fracture

School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, Hu'nan, China

摘要

摘要: 提出一种分析弹性固体动态断裂的多尺度扩展有限元方法。该方法采用局部网格细化对网格模型中裂纹部分进行处理, 并利用可变结点单元连接不同尺度网格单元, 在提高数值计算精度的基础上, 节省了计算成本; 利用隐式Newmark时间积分和相互作用积分求动应力强度因子。通过算例数值计算结果与已有文献结果进行对比, 验证方法优劣性。结果表明: 多尺度扩展有限元方法是模拟弹性结构动断裂的一种有效数值方法, 相较于标准扩展有限元方法具有更高的精度。
- 动态断裂 /
- 扩展有限元 /
- 可变结点单元 /
- 动应力强度因子
Abstract: A multi-scale extend finite element method (XFEM) for analyzing the dynamic fracture of elastic solids is proposed. The present method uses local mesh refinement to process the cracks in the mesh model, and variable-node elements is used to connect different scale mesh elements, which saves calculation costs on the basis of improving the accuracy of numerical calculations; implicit Newmark time integration and the interaction integral is used to solve the dynamic intensity factor. The calculated results of the calculation examples are compared with those of the existing literature to verify the pros and cons of the method. The results show that the multi-scale XFEM is an effective numerical method for simulating the dynamic fracture of elastic structures, and it has higher accuracy than the standard XFEM.
- dynamic fracture /
- XFEM /
- variable-node elements /
- dynamic stress intensity factor

HTML全文

图 1 二维裂纹问题示意图

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图 2 裂纹结点分布图

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图 3 多尺度网格示意图

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图 4 (4+k+l+m+n)结点单元示意图

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图 5 J积分轮廓图

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图 6 Ⅰ型裂纹计算模型示意图

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图 7 不同方法归一化动强度因子结果比较

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图 8 不同方法归一化动强度因子结果比较

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图 9 半无限板网格示意图

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图 10 边界斜裂纹板示意图

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图 11 边界斜裂纹板网格示意图

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图 12 不同方法归一化动强度因子结果比较

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表 1 算例运算时间记录表

方法	单元	自由度	运算时间/s
扩展有限元(65×25)	1 625	3 592	11.346 863
扩展有限元(79×41)	3 239	6 908	14.317 028
扩展有限元(195×75)	14 625	30 212	71.641 841
多尺度扩展有限元	3 025	6 812	24.890 456

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参考文献(19)

[1]	岳中文, 宋耀, 杨仁树, 等. 冲击荷载下深梁动态断裂行为的光弹性实验[J]. 振动与冲击, 2017, 36(19): 236-241 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201719036.htm YUE Z W, SONG Y, YANG R S, et al. Photoelastic experiments on deep beam fracture behaviors under impact load[J]. Journal of Vibration and Shock, 2017, 36(19): 236-241 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201719036.htm
[2]	柳占立, 初东阳, 王涛, 等. 动态断裂数值模拟及工程应用[C]//2018年全国固体力学学术会议摘要集(上). 桐乡: 中国力学学会, 2018: 138 LIU Z L, CHU D Y, WANG T, et al. Numerical simulation of dynamic fracture and engineering application[C]//Abstract Collection of 2018 National Solid Mechanics Conference (Part 1). Tongxiang: Chinese Society of Mechanics, 2018: 138 (in Chinese)
[3]	李清, 张迪, 杨阳, 伟东等. 含单侧预制裂纹梁的冲击动态断裂过程试验研究[J]. 振动与冲击, 2015, 34(4): 205-210 LI Q, ZHANG D, YANG Y, et al. Dynamic fracture tests for a beam containing unilateral pre-existing cracks under impact loads[J]. Journal of Vibration and Shock, 2015, 34(4): 205-210 (in Chinese)
[4]	岳中文, 宋耀, 陈彪, 等. 冲击载荷下层状岩体动态断裂行为的模拟试验研究[J]. 振动与冲击, 2017, 36(12): 223-229 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201712036.htm YUE Z W, SONG Y, CHEN B, et al. A study on the behaviors of dynamic fracture in layered rocks under impact loading[J]. Journal of Vibration and Shock, 2017, 36(12): 223-229 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201712036.htm
[5]	岳中文, 宋耀, 邱鹏, 等. 冲击载荷下双预置裂纹三点弯曲梁动态断裂实验[J]. 振动与冲击, 2017, 36(4): 151-156, 177 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201704024.htm YUE Z W, SONG Y, QIU P, et al. A dynamic fracture experiment of a three-point-bend beam containing double pre-existing cracks under impact load[J]. Journal of Vibration and Shock, 2017, 36(4): 151-156, 177 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201704024.htm
[6]	杨仁树, 苏洪, 陈程, 等. 相互贯通裂纹动态断裂的试验研究[J]. 振动与冲击, 2017, 36(13): 134-139 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201713023.htm YANG R S, SU H, CHEN C, et al. Tests for dynamic fracture of interconnected cracks[J]. Journal of Vibration and Shock, 2017, 36(13): 134-139 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201713023.htm
[7]	钟红, 马振洲, 胡少伟, 等前混凝土/花岗岩界面动态断裂性能的轴拉试验研究[J]. 振动与冲击, 2019, 38(11): 152-158 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201911024.htm ZHONG H, MA Z Z, HU S W, et al. Axial tensile tests for dynamic fracture characteristics of concrete-granite interface[J]. Journal of Vibration and Shock, 2019, 38(11): 152-158 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201911024.htm
[8]	SHARMA A, KUMAR S A, KUSHVAHA V. Effect of aspect ratio on dynamic fracture toughness of particulate polymer composite using artificial neural network[J]. Engineering Fracture Mechanics, 2020, 228: 106907 doi: 10.1016/j.engfracmech.2020.106907
[9]	SONG J H, WANG H W, BELYTSCHKO T. A comparative study on finite element methods for dynamic fracture[J]. Computational Mechanics, 2008, 42(2): 239-250 doi: 10.1007/s00466-007-0210-x
[10]	MENOUILLARD T, BELYTSCHKO T. Dynamic fracture with meshfree enriched XFEM[J]. Acta Mechanica, 2010, 213(1-2): 53-69 doi: 10.1007/s00707-009-0275-z
[11]	ASAREH I, YOON Y C, SONG J H. A numerical method for dynamic fracture using the extended finite element method with non-nodal enrichment parameters[J]. International Journal of Impact Engineering, 2018, 121: 63-76 doi: 10.1016/j.ijimpeng.2018.06.012
[12]	ZENG Q, MOTAMEDI M H, LEONG A F T, et al. Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM[J]. International Journal of Fracture, 2019, 215(1-2): 49-65 doi: 10.1007/s10704-018-0330-7
[13]	YIN S H, YU T T, BUI T Q, et al. Static and dynamic fracture analysis in elastic solids using a multiscale extended isogeometric analysis[J]. Engineering Fracture Mechanics, 2019, 207: 109-130 doi: 10.1016/j.engfracmech.2018.12.024
[14]	TENG Z H, LIAO D M, WU S C, et al. An adaptively refined XFEM for the dynamic fracture problems with micro-defects[J]. Theoretical and Applied Fracture Mechanics, 2019, 103: 102255 doi: 10.1016/j.tafmec.2019.102255
[15]	底月兰, 王海斗, 董丽虹, 等. 扩展有限元法在裂纹扩展问题中的应用[J]. 材料导报, 2017, 31(3): 70-74, 85 https://www.cnki.com.cn/Article/CJFDTOTAL-CLDB201703012.htm DI Y L, WANG H D, DONG L H, et al. Application of the extended finite element method in crack propagation[J]. Materials Guide, 2017, 31(3): 70-74, 85 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CLDB201703012.htm
[16]	LIM J H, SOHN D, IM S. Variable-node element families for mesh connection and adaptive mesh computation[J]. Structural Engineering and Mechanics, 2012, 43(3): 349-370 doi: 10.12989/sem.2012.43.3.349
[17]	LIU P, BUI T Q, ZHANG C, et al. The singular edge-based smoothed finite element method for stationary dynamic crack problems in 2D elastic solids[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 233-236: 68-80 doi: 10.1016/j.cma.2012.04.008
[18]	WU L, LIU P, SHI C, et al. Edge-based smoothed extended finite element method for dynamic fracture analysis[J]. Applied Mathematical Modelling, 2016, 40(19-20): 8564-8579 doi: 10.1016/j.apm.2016.05.027
[19]	MENOUILLARD T, BELYTSCHKO T. Dynamic fracture with meshfree enriched XFEM[J]. Acta Mechanica, 2010, 213(1-2): 53-69 doi: 10.1007/s00707-009-0275-z