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考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

金浩 余朔

金浩, 余朔. 考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法. 力学学报, 2021, 53(10): 2805-2814 doi: 10.6052/0459-1879-21-272
引用本文: 金浩, 余朔. 考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法. 力学学报, 2021, 53(10): 2805-2814 doi: 10.6052/0459-1879-21-272
Jin Hao, Yu Shuo. Cdm-xfem method for crack calculation considered plastic dissipation of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2805-2814 doi: 10.6052/0459-1879-21-272
Citation: Jin Hao, Yu Shuo. Cdm-xfem method for crack calculation considered plastic dissipation of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2805-2814 doi: 10.6052/0459-1879-21-272

考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

doi: 10.6052/0459-1879-21-272
基金项目: 国家自然科学基金(51908428)和江苏省自然科学基金(BK20211173)资助项目
详细信息
    作者简介:

    金浩, 副研究员, 研究方向: (城市)轨道交通振动工程. E-mail: jinhao@seu.edu.cn

  • 中图分类号: TU311.4

CDM-XFEM METHOD FOR CRACK CALCULATION CONSIDERED PLASTIC DISSIPATION OF CONCRETE

  • 摘要: 混凝土结构在服役期间受外界荷载的影响容易产生裂缝, 导致结构刚度降低、构件承载性能衰退, 而采用准确的计算方法预测混凝土裂缝的发展是治理裂缝的基本前提, 也是保障结构安全的重要手段. CDM方法能够描述微裂缝的扩展过程, 但不能表示离散的开裂面, 且存在网格诱导偏差及虚假应力传递的弊端, XFEM方法能够描述宏观裂纹的扩展过程, 但不能反映微裂缝的动态扩展, 两者计算出的裂纹分布与实际差异均较大. 现有的CDM-XFEM方法已经能够模拟混凝土微裂缝及宏观裂缝发展的整个过程, 但忽略了宏观裂缝出现时混凝土产生的塑性应变, CDM与XFEM的能量转化过程欠缺平衡性. 因此, 本文重点考虑能量转化时的塑性耗散, 选取指数型函数为粘结裂缝的牵引-分离模式, 基于能量及应力等效的条件重新构建了CDM与XFEM之间的能量转化方程. 采用广义逆最小二乘法求解能量转化系数, 确定能量转化时的临界位移, 并给出了裂缝面水平集的更新算法及整体计算方法的程序流程. 以双切口混凝土受剪拉开裂试验为例, 采用多种裂缝计算方法与试验进行了对比. 结果表明, 采用考虑混凝土塑性耗散的CDM-XFEM方法算出的裂缝分布及拉力-张开位移曲线与试验结果差异最小, 说明采用考虑混凝土塑性耗散的CDM-XFEM计算方法能够更好地计算混凝土裂缝.

     

  • 图  1  CDM-XFEM方法计算过程示意图

    Figure  1.  Calculation process CDM-XFEM method

    图  2  CDM的应力-应变曲线

    Figure  2.  Stress-strain curve of CDM

    图  3  XFEM粘结裂缝的牵引-分离曲线

    Figure  3.  Traction-separation curve of XFEM cohesive crack

    图  4  考虑混凝土塑性耗散的CDM-XFEM方法计算流程

    Figure  4.  Calculation flow of CDM-XFEM method considered concrete plastic dissipation

    图  5  裂缝水平集函数速度分量示意图

    Figure  5.  Velocity component of crack level set function

    图  6  双切口混凝土受剪拉开裂试验[45]

    Figure  6.  Shear tensile cracking test of concrete contained double notched[45]

    图  7  试验与各种方法算出的裂缝分布对比

    Figure  7.  Comparison of crack distribution calculated by various methods and experiment

    图  8  考虑塑性耗散的CDM-XFEM计算出的三维裂缝分布云图

    Figure  8.  3D crack distribution calculated by CDM-XFEM considered plastic dissipation

    图  9  试验与各种方法算出的拉力-张开位移曲线对比

    Figure  9.  Comparison of the tension-open displacement curves obtained by experiment and various calculation methods

  • [1] 徐纪鹏, 董新龙, 付应乾等. 不同加载边界下混凝土巴西劈裂过程及强度的DIC实验分析. 力学学报, 2020, 52(3): 864-876 (Xu jipeng, Dong Xinlong, Fu Yingqian, et al. Experimental analysis of process and tensile strength for concrete Brazilian splitting test with different loading boundaries by DIC method. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(3): 864-876 (in Chinese) doi: 10.6052/0459-1879-19-303
    [2] 吴建营, 陈万昕, 黄羽立. 基于统一相场理论的早龄期混凝土化-热-力多场耦合裂缝模拟与抗裂性能预测. 力学学报, 2021, 53(5): 1367-1382 (Wu Jianying, Chen Wanxin, Huang Yuli. Computational modeling of shrinkage induced cracking in early-age concrete based on the unified phase-field theory. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1367-1382 (in Chinese) doi: 10.6052/0459-1879-21-020
    [3] Yu S, Jin H. Modeling of the corrosion-induced crack in concrete contained transverse crack subject to chloride ion penetration. Construction and Building Materials, 2020, 258: 119645 doi: 10.1016/j.conbuildmat.2020.119645
    [4] 余朔, 金浩, 毕湘利. 荷载裂缝几何形态对管片外排钢筋锈层分布的影响. 工程力学, 2020, 37(4): 118-128 (Yu Shuo, Jin Hao, Bi Xiangli. Effect of geometry form of load crack on rust layer distribution of outside steel in segment. Engineering Mechanics, 2020, 37(4): 118-128 (in Chinese)
    [5] Simone A, Wells G, Sluys L. From continuous to discontinuous failure in a gradient-enhanced continuum damage model. Computer Methods in Applied Mechanics and Engineering, 2003, 192: 4581-4607 doi: 10.1016/S0045-7825(03)00428-6
    [6] Li X, Chen J. An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials. Computer Methods in Applied Mechanics and Engineering, 2017, 315: 744-759 doi: 10.1016/j.cma.2016.11.029
    [7] Tamayo E, Rodriguez A. A new continuous–discontinuous damage model: Cohesive cracks via an accurate energy-transfer process. Theoretical and Applied Fracture Mechanics, 2014, 69: 90-101 doi: 10.1016/j.tafmec.2013.11.009
    [8] Challamel N. A variationally based nonlocal damage model to predict diffuse microcracking evolution. International Journal of Mechanical Sciences, 2010, 52: 1783-1800 doi: 10.1016/j.ijmecsci.2010.09.012
    [9] 李忠友, 刘元雪, 姚志华等. 基于能量耗散原理的混凝土力学损伤模型. 土木工程学报, 2019, 52(S1): 23-30 (Li Zhongyou, Liu Yuanxue, Yao Zhihua, et al. Mechanical damage model for concrete based on energy dissipation. China Civil Engineering Journal, 2019, 52(S1): 23-30 (in Chinese)
    [10] Vilppo J, Kouhia R, Hartikainen J, et al. Anisotropic damage model for concrete and other quasi-brittle materials. International Journal of Solids and Structures, 2021, 225: 111048 doi: 10.1016/j.ijsolstr.2021.111048
    [11] Poliotti M, Bairan J. A new concrete plastic-damage model with an evolutive dilatancy parameter. Engineering Structures, 2019, 189: 541-549 doi: 10.1016/j.engstruct.2019.03.086
    [12] Pereira L, Weerheijm B, Sluys L. A numerical study on crack branching in quasi-brittle materials with a new effective rate-dependent nonlocal damage model. Engineering Fracture Mechanics, 2017, 182: 689-707 doi: 10.1016/j.engfracmech.2017.06.019
    [13] Xia X, Chen F, Gu X, et al. Interfacial debonding constitutive model and XFEM simulation for mesoscale concrete. Computers and Structures, 2021, 242: 106373 doi: 10.1016/j.compstruc.2020.106373
    [14] 杨涛, 邹道勤. 基于XFEM的钢筋混凝土梁开裂数值模拟. 浙江大学学报(工学版), 2013, 47(3): 495-501 (Yang Tao, Zou Daoqin. Numerical simulation of crack growth of reinforced concrete beam based on XFEM. Journal of Zhejiang University (Engineering Science) , 2013, 47(3): 495-501 (in Chinese) doi: 10.3785/j.issn.1008-973X.2013.03.014
    [15] Agathos K, Ventura G, Chatzi E, et al. Stable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes. International Journal for Numerical Methods in Engineering, 2017, 113: 252-276
    [16] Schaetzer M, Fries T. Loaded crack surfaces in two and three dimensions with XFEM. Applied Mathematical Modelling, 2020, 78: 863-885 doi: 10.1016/j.apm.2019.10.020
    [17] Haghani M, Neya B, Ahmadi M, et al. Combining XFEM and Time Integration by α-Method for Seismic Analysis of Dam-Foundation-Reservoir. Theoretical and Applied Fracture Mechanics, 2020, 109: 102752 doi: 10.1016/j.tafmec.2020.102752
    [18] Cervera M, Chiumenti M. Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique. Computer Methods in Applied Mechanics and Engineering, 2006, 196: 304-320 doi: 10.1016/j.cma.2006.04.008
    [19] Jirásek M, Grassl P. Evaluation of directional mesh bias in concrete fracture simulations using continuum damage models. Engineering Fracture Mechanics, 2008, 75: 1921-1943 doi: 10.1016/j.engfracmech.2007.11.010
    [20] Slobbe A, Hendriks M, Rots J. Systematic assessment of directional mesh bias with periodic boundary conditions: Applied to the crack band model. Engineering Fracture Mechanics, 2013, 109: 186-208 doi: 10.1016/j.engfracmech.2013.06.005
    [21] Faron A, Rombach G. Simulation of crack growth in reinforced concrete beams using extended finite element method. Engineering Failure Analysis, 2020, 116: 104698 doi: 10.1016/j.engfailanal.2020.104698
    [22] Roth S, Léger P, Soulaimani A. Strongly coupled XFEM formulation for non-planar three-dimensional simulation of hydraulic fracturing with emphasis on concrete dams. Computer Methods in Applied Mechanics and Engineering, 2020, 363: 112899 doi: 10.1016/j.cma.2020.112899
    [23] Comi C, Mariani S, Perego U. An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31: 213-238 doi: 10.1002/nag.537
    [24] Jin W, Arson C. XFEM to couple nonlocal micromechanics damage with discrete mode I cohesive fracture. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112617 doi: 10.1016/j.cma.2019.112617
    [25] Pandey V, Singh I, Mishra B, et al. A new framework based on continuum damage Mechanics and XFEM for high cycle fatigue crack growth simulations. Engineering Fracture Mechanics, 2019, 206: 172-200 doi: 10.1016/j.engfracmech.2018.11.021
    [26] Serpieri R, Albarella M, Sacco E. A 3D two-scale multiplane cohesive-zone model for mixed-mode fracture with finite dilation. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 857-888 doi: 10.1016/j.cma.2016.10.021
    [27] Santos F, Sousa J. A viscous-cohesive model for concrete fracture in quasi-static loading rate. Engineering Fracture Mechanics, 2020, 228: 106893 doi: 10.1016/j.engfracmech.2020.106893
    [28] Venzal V, Morel S, Parent T, et al. Frictional cohesive zone model for quasi-brittle fracture: Mixed-mode and coupling between cohesive and frictional behaviors. International Journal of Solids and Structures, 2020, 198: 17-30 doi: 10.1016/j.ijsolstr.2020.04.023
    [29] Roth S, Léger P, Soulaimani A. A combined XFEM–damage mechanics approach for concrete crack propagation. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 923-955 doi: 10.1016/j.cma.2014.10.043
    [30] Bobinski J, Tejchman J, et al. A coupled constitutive model for fracture in plain concrete based on continuum theory with non-local softening and eXtended Finite Element Method. Finite Elements in Analysis and Design, 2016, 114: 1-21 doi: 10.1016/j.finel.2016.02.001
    [31] Wang Y, Waisman H. From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials. Computer Methods in Applied Mechanics and Engineering, 2016, 299: 57-89 doi: 10.1016/j.cma.2015.10.019
    [32] Omidi O, Lotfi V. Continuum large cracking in a rate-dependent plastic-damage model for cyclic-loaded concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37: 1363-1390 doi: 10.1002/nag.2093
    [33] Ahmed B, Voyiadjis G, Park T. Damaged plasticity model for concrete using scalar damage variables with a novel stress decomposition. International Journal of Solids and Structures, 2020, 191: 56-75
    [34] Pass M, Schreurs P, Brekelmans W. A continuum approach to brittle and fatigue damage: Theory and numerical procedures. International Journal of Solids and Structures, 1993, 30(4): 579-599 doi: 10.1016/0020-7683(93)90189-E
    [35] Gunn R. Non-linear analysis of arch dams including an anisotropic damage mechanics based constitutive model for concrete[PhD Thesis]. England: University of Brighton, 1998.
    [36] Jirásek M, Desmorat R. Localization analysis of nonlocal models with damage-dependent nonlocal interaction. International Journal of Solids and Structures, 2019, 174-175: 1-17 doi: 10.1016/j.ijsolstr.2019.06.011
    [37] Hatzigeorgiou G, Beskos D, Theodorakopoulos D, et al. A simple concrete damage model for dynamic FEM applications. International Journal of Computational Engineering Science, 2001, 2(2): 267-286 doi: 10.1142/S1465876301000325
    [38] Nikolakopoulos K, Crete J, Longere P. Volume averaging based integration method in the context of XFEM-cohesive zone model coupling. Mechanics Research Communications, 2020, 104: 103485 doi: 10.1016/j.mechrescom.2020.103485
    [39] Santos F, Sousa J. A viscous-cohesive model for concrete fracture in quasi-static loading rate. Engineering Fracture Mechanics, 2020, 228: 106893 doi: 10.1016/j.engfracmech.2020.106893
    [40] 魏木生, 李莹, 赵建立. 广义最小二乘问题的理论和计算(第2版). 北京: 科学出版社, 2020

    Wei Musheng, Li Ying, Zhao Jianli. Theory and calculation of generalized least squares problem(the second edition). Beijing: Science Press, 2020 (in Chinese)
    [41] Sadeghirad A, Chopp D, Ren X, et al. A novel hybrid approach for level set characterization and tracking of non-planar 3D cracks in the extended finite element method. Engineering Fracture Mechanics, 2016, 160: 1-14 doi: 10.1016/j.engfracmech.2016.03.027
    [42] Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets—Part II: Level set update. International Journal for Numerical Methods in Engineering, 2002, 53: 2569-2586 doi: 10.1002/nme.430
    [43] Peng D, Merriman B, Osher S, et al. A PDE-based fast local level set method. Journal of Computational Physics, 1999, 155(2): 410-438 doi: 10.1006/jcph.1999.6345
    [44] Colombo D, Massin P. Fast and robust level set update for 3D non-planar X-FEM crack propagation modelling. Computer Methods in Applied Mechanics and Engineering, 2011, 200: 2160-2180 doi: 10.1016/j.cma.2011.03.014
    [45] Nooru-Mohamed M. Mixed-mode fracture of concrete: An experimental approach[PhD Thesis]. Netherlands : Technische Universiteit, 1992.
    [46] Shi J, Chopp D, Lua J, et al. Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions. Engineering Fracture Mechanics, 2010, 77: 2840-2863 doi: 10.1016/j.engfracmech.2010.06.009
    [47] Yin Y, Ren Q, Shen L. Study on the effect of aggregate distribution on mechanical properties and damage cracks of concrete based on multifractal theory. Construction and Building Materials, 2020, 262: 120086 doi: 10.1016/j.conbuildmat.2020.120086
    [48] Ghosh S, Dhang N, Deb A. Influence of aggregate geometry and material fabric on tensile cracking in concrete. Engineering Fracture Mechanics, 2020, 239: 107321 doi: 10.1016/j.engfracmech.2020.107321
    [49] Nitka M, Tejchman J. Meso-mechanical modelling of damage in concrete using discrete element method with porous ITZs of defined width around aggregates. Engineering Fracture Mechanics, 2020, 231: 107029 doi: 10.1016/j.engfracmech.2020.107029
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出版历程
  • 收稿日期:  2021-06-16
  • 录用日期:  2021-09-24
  • 网络出版日期:  2021-09-25

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