• 全国中文核心期刊
  • 中国科技核心期刊
  • 美国工程索引(EI)收录期刊
  • Scopus数据库收录期刊
ZHOU Xiao-ping, JIA Zhi-ming. Field-enriched finite element method for numerical simulation of initiation, propagation and coalescence of multiple cracks[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(6): 988-996. DOI: 10.11779/CJGE202206002
Citation: ZHOU Xiao-ping, JIA Zhi-ming. Field-enriched finite element method for numerical simulation of initiation, propagation and coalescence of multiple cracks[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(6): 988-996. DOI: 10.11779/CJGE202206002

Field-enriched finite element method for numerical simulation of initiation, propagation and coalescence of multiple cracks

More Information
  • Received Date: July 11, 2021
  • Available Online: September 22, 2022
  • The study on the mechanical response and cracking behaviors of brittle rock materials with multiple cracks is of vital significance for the design and stability analysis of rock engineering structures. A field-enriched finite element method (FE-FEM) is proposed to study the evolution behaviors of multiple cracks in rock materials, including crack initiation, propagation and coalescence. The solutions to the crack coalescence problem during simulation are proposed. The field-enriched finite element method can directly deal with the complex multiple crack problem, while the extra enriched function needs to be introduced in the extended finite element method (XFEM). The analytical results of the present numerical examples demonstrate that the proposed numerical method has the capability to handle complex multiple crack propagation and coalescence.
  • [1]
    FREIJ-AYOUB R, DYSKIN A V, GALYBIN A N. The dislocation approximation for calculating crack interaction[J]. International Journal of Fracture, 1997, 86(4): 57–62.
    [2]
    RYBACZUK M, STOPPEL P. The fractal growth of fatigue defects in materials[J]. International Journal of Fracture, 2000, 103(1): 71–94. doi: 10.1023/A:1007635717332
    [3]
    CHEN Y Z. General case of multiple crack problems in an infinite plate[J]. Engineering Fracture Mechanics, 1984, 20(4): 591–597. doi: 10.1016/0013-7944(84)90034-1
    [4]
    CHENG H, ZHOU X P, ZHU J, et al. The effects of crack openings on crack initiation, propagation and coalescence behavior in rock-like materials under uniaxial compression[J]. Rock Mechanics and Rock Engineering, 2016, 49(9): 3481–3494. doi: 10.1007/s00603-016-0998-9
    [5]
    ZHANG J Z, ZHOU X P. AE event rate characteristics of flawed granite: from damage stress to ultimate failure[J]. Geophysical Journal International, 2020, 222(2): 795–814. doi: 10.1093/gji/ggaa207
    [6]
    CARPINTERI A, MONETTO I. Snap-back analysis of fracture evolution in multi-cracked solids using boundary element method[J]. International Journal of Fracture, 1999, 98(3/4): 225–241. doi: 10.1023/A:1018660600546
    [7]
    DENDA M, DONG Y F. Complex variable approach to the BEM for multiple crack problems[J]. Computer Methods in Applied Mechanics and Engineering, 1997, 141(3/4): 247–264.
    [8]
    BUDYN E, ZI G, MOËS N, et al. A method for multiple crack growth in brittle materials without remeshing[J]. International Journal for Numerical Methods in Engineering, 2004, 61(10): 1741–1770. doi: 10.1002/nme.1130
    [9]
    ZHOU X P, CHEN J W. Extended finite element simulation of step-path brittle failure in rock slopes with non-persistent en-echelon joints[J]. Engineering Geology, 2019, 250: 65–88. doi: 10.1016/j.enggeo.2019.01.012
    [10]
    WANG Y T, ZHOU X P, WANG Y, et al. A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids[J]. International Journal of Solids and Structures, 2018, 134: 89–115. doi: 10.1016/j.ijsolstr.2017.10.022
    [11]
    AZADI H, KHOEI A R. Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing[J]. International Journal for Numerical Methods in Engineering, 2011, 85(8): 1017–1048. doi: 10.1002/nme.3002
    [12]
    ZHOU X P, FU L, QIAN Q H. A 2D novel non-local lattice bond model for initiation and propagation of cracks in rock materials[J]. Engineering Analysis with Boundary Elements, 2021, 126: 181–199. doi: 10.1016/j.enganabound.2021.03.002
    [13]
    ZHOU X P, BI J, QIAN Q H. Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws[J]. Rock Mechanics and Rock Engineering, 2015, 48(3): 1097–1114. doi: 10.1007/s00603-014-0627-4
    [14]
    JIA Z M, ZHOU X P, BERTO F. Compressive-shear fracture model of the phase-field method coupled with a modified Hoek–Brown criterion[J]. International Journal of Fracture, 2021, 229(2): 161–184. doi: 10.1007/s10704-021-00546-7
    [15]
    XU D D, WU A Q, LI C. A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2019, 11(6): 1256–1263. doi: 10.1016/j.jrmge.2019.02.007
    [16]
    石路杨, 余天堂. 多裂纹扩展的扩展有限元法分析[J]. 岩土力学, 2014, 35(1): 263–272. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201401040.htm

    SHI Lu-yang, YU Tian-tang. Analysis of multiple crack growth using extended finite element method[J]. Rock and Soil Mechanics, 2014, 35(1): 263–272. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201401040.htm
    [17]
    BARBIERI E, PETRINIC N, MEO M, et al. A new weight-function enrichment in meshless methods for multiple cracks in linear elasticity[J]. International Journal for Numerical Methods in Engineering, 2012, 90(2): 177–195. doi: 10.1002/nme.3313
    [18]
    RABCZUK T, BORDAS S, ZI G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics[J]. Computational Mechanics, 2007, 40(3): 473–495. doi: 10.1007/s00466-006-0122-1
    [19]
    YAU J F, WANG S S, CORTEN H T. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity[J]. Journal of Applied Mechanics, 1980, 47(2): 335–341. doi: 10.1115/1.3153665
    [20]
    SHIH C F, ASARO R J. Elastic-plastic analysis of cracks on bimaterial interfaces: part Ⅰ—small scale yielding[J]. Journal of Applied Mechanics, 1988, 55(2): 299–316. doi: 10.1115/1.3173676
    [21]
    ERDOGAN F, SIH G C. Closure to "discussion of 'on the crack extension in plates under plane loading and transverse shear'"[J]. Journal of Basic Engineering, 1963, 85(4): 527. doi: 10.1115/1.3656899
    [22]
    ZHOU X P, JIA Z M, WANG L F. A field-enriched finite element method for brittle fracture in rocks subjected to mixed mode loading[J]. Engineering Analysis with Boundary Elements, 2021, 129: 105–124. doi: 10.1016/j.enganabound.2021.04.023
    [23]
    SUKUMAR N, PRÉVOST J H. Modeling quasi-static crack growth with the extended finite element method Part Ⅰ: computer implementation[J]. International Journal of Solids and Structures, 2003, 40(26): 7513–7537. doi: 10.1016/j.ijsolstr.2003.08.002
    [24]
    MOËS N, DOLBOW J, BELYTSCHKO T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150. doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
    [25]
    刘丰, 郑宏, 李春光. 基于NMM的EFG方法及其裂纹扩展模拟[J]. 力学学报, 2014, 46(4): 582–590. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201404012.htm

    LIU Feng, ZHENG Hong, LI Chun-guang. The nmm-based efg method and simulation of crack propagation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(4): 582–590. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201404012.htm
    [26]
    PALUSZNY A, MATTHÄI S K. Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media[J]. International Journal of Solids and Structures, 2009, 46(18/19): 3383–3397.
    [27]
    CIVELEK M B, ERDOGAN F. Crack problems for a rectangular plate and an infinite strip[J]. International Journal of Fracture, 1982, 19(2): 139–159. doi: 10.1007/BF00016570
  • Related Articles

    [1]LIANG Xiaomin, GU Xiaoqiang, ZHAI Chongpu, WEI Deheng. Anisotropic wave velocities of granular materials and microscopic fabric using X-ray computed tomography[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(7): 1398-1407. DOI: 10.11779/CJGE20230425
    [2]ZHANG He-nian, CHEN Liang, LI Xiong-wei, XI Pei-sheng, MU Lin, HU Cai-yun. Ratio and mechanism of activated magnesium oxide carbonized raw earth block materials[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(S2): 233-236. DOI: 10.11779/CJGE2021S2055
    [3]YAO Jun-kai, YE Yang-sheng, WANG Peng-cheng, CHEN Feng, CAI De-gou. Subgrade heave of sulfate attacking on cement-stabilized filler[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(4): 782-788. DOI: 10.11779/CJGE201904024
    [4]XU Xiao-li, GAO Feng, ZHANG Zhi-zhen, ZHANG Chuan-hu. Energy and structural effects of granite after high temperature[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(5): 961-968. DOI: 10.11779/CJGE201405022
    [5]ZHOU Qiao-yong, XIONG Bao-lin, YANG Guang-qing, LIU Wei-chao. Microstructure of low liquid limit silt[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 439-444.
    [6]YU Hui, DING Xuan-ming, KONG Gang-qiang, ZHENG Chang-jie. Comparative FEM analysis of deformation properties of expressway widening projects with cast-in-situ X-shaped concrete piles and circular pile[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 170-176.
    [7]WANG Cheng-hu, WANG Hong-cai, LIU Li-peng, SUN Dong-sheng, ZHAO Wei-hua. Effects of high temperatures on mechanical performance of basaltic tuff and mechanism analysis[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(10): 1827-1835.
    [8]Micro-experiments on a soft ground improved by cement-mixed soils with gypsum additive[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(8).
    [9]Full scale model tests on vertical bearing characteristics of cast-in-place X-section piles[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(6).
    [10]WU Yanqing, CAO Guangzhu, DING Weihua. Permeability experiment of sandstone under variable seepage pressures by using X-ray CT real-time observation[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(7): 780-785.
  • Cited by

    Periodical cited type(4)

    1. 王大兵,黄郁东,韩振中,徐考,崔文海,周苏华. 基于贝叶斯逻辑回归模型的边坡稳定性预测. 市政技术. 2023(10): 173-180 .
    2. 曾锃,赵树祥,葛龙进,潘卫平,李敏,殷国峰. 罗闸河二级水电站拱坝右岸边坡变形破坏机制研究及治理后评估. 岩土工程学报. 2021(S1): 171-175 . 本站查看
    3. 夏增选,李萍,曹博,李同录,沈伟,康海伟. 边坡可靠度的Bayes估计及后验稳健性. 河海大学学报(自然科学版). 2020(03): 238-244 .
    4. 谢永利,刘新荣,晏长根,杨忠平,李家春,周志军,岳夏冰. 特殊岩土体工程边坡研究进展. 土木工程学报. 2020(09): 93-105 .

    Other cited types(18)

Catalog

    Article views (215) PDF downloads (198) Cited by(22)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return