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浙江大学学报(工学版)
浙江大学学报(工学版)  2018, Vol. 52 Issue (3): 497-503    DOI: 10.3785/j.issn.1008-973X.2018.03.011
机械工程与力学     
脆性多裂纹扩展问题的近场动力学建模分析
秦洪远, 刘一鸣, 黄丹
河海大学 工程力学系, 江苏 南京 211100
Peridynamic modelling and simulation for multiple crack propagation in brittle materials
QIN Hong-yuan, LIU Yi-ming, HUANG Dan
Department of Engineering Mechanics, Hohai University, Nanjing 211100, China
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摘要：

针对脆性多裂纹扩展问题，基于近场动力学（PD）理论开展本构建模与数值方法研究.在常规微弹脆性本构模型基础上引入物质点对的转动，同时在本构力模型中增加能够反映物质点间长程力尺寸效应的核函数，提高计算精度、效率和结果的稳定性.构建能够以统一的模型和算法自然模拟脆性多裂纹扩展全过程的PD数值体系.通过定量分析确定最佳近场尺寸及核函数，通过双裂纹巴西圆盘和多裂纹脆性板的破坏过程模拟验证所提模型和算法，结果表明：改进型PD模型和数值方法可以定性、定量分析脆性多裂纹扩展问题.模拟单轴拉伸荷载作用下双裂纹脆性板的裂纹扩展过程，得到了初始裂纹分布情况对结构破坏形式和承载能力的影响规律.
Abstract:

An improved peridynamic (PD) constitutive model and corresponding numerical method were proposed to analyze the multiple crack propagation in brittle materials. The rotation of the bond of material points was introduced into the conventional microelastic brittle PD model; a kernel function reflecting the internal length effect of long-range forces between material points was implemented into the constitutive force model, to improve the accuracy, efficiency and stability of calculation. Meanwhile, a numerical system under the framework of PD was developed to simulate the multiple crack propagation in brittle materials naturally with the uniform model and algorithms. The most effective peridynamic horizon size and kernel function were confirmed through quantitative analysis. The proposed model and algorithms were validated through the disruptive process simulation of a double-notched Brazilian disk and a brittle plate with multiple cracks. Results show that the improved PD model and numerical method can analyze the brittle crack propagation problem, qualitatively and quantitatively. Moreover, the crack propagation in a brittle plate with two pre-existing cracks under uniaxial tension was analyzed, then the influence rule of the initial cracks' distribution on the stucture's failure mode and failure load is discovered.
收稿日期: 2017-05-23 出版日期: 2018-09-11
CLC:  O346.1  
基金资助:

国家自然科学基金资助项目（51679077，11132003）；江苏省自然科学基金资助项目（BK20130822）；中央高校基本科研业务费资助项目（2015B18314，2017B13014）；NSFC-广东联合基金（第二期）超级计算科学应用研究专项资助.
通讯作者: 黄丹,男,教授.orcid.org/0000-0002-5252-5832.     E-mail: danhuang@hhu.edu.cn
作者简介: 秦洪远(1993-),男,硕士生,从事岩土工程和计算力学研究.orcid.org/0000-0003-1073-7025.E-mail:hhuhongyuan_qin@foxmail.com.
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引用本文:

秦洪远, 刘一鸣, 黄丹. 脆性多裂纹扩展问题的近场动力学建模分析[J]. 浙江大学学报(工学版), 2018, 52(3): 497-503.

QIN Hong-yuan, LIU Yi-ming, HUANG Dan. Peridynamic modelling and simulation for multiple crack propagation in brittle materials. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2018, 52(3): 497-503.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2018.03.011    或    http://www.zjujournals.com/eng/CN/Y2018/V52/I3/497

[1] WONG R H C, CHAU K T, TANG C A, et al. Analysis of crack coalescence in rock-like materials containing three flaws, Part I:experimental approach[J]. International Journal of Rock Mechanics & Mining Sciences, 2012, 38(7):909-924.
[2] 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. 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.
[3] 刘丰, 郑宏, 夏开文. 基于MLS的数值流形法模拟多裂纹扩展[J]. 岩石力学与工程学报, 2016, 35(1):76-86. LIU Feng, ZHENG Hong, XIA Kai-wen. The MLS-based numerical manifold method and its applications to multiple crack propagation[J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35(1):76-86.
[4] BUDYN É, ZI G, MOES 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.
[5] SILLING S A. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the Mechanics and Physics of Solids, 2000, 48(1):175-209.
[6] 黄丹, 章青, 乔丕忠, 等. 近场动力学方法及其应用[J]. 力学进展, 2010, 40(4):448-459. HUANG Dan, ZHANG Qing, QIAO Pi-zhong, et al. A review on peridynamics method and its application[J]. Advance in Mechanics, 2010, 40(4):448-459.
[7] 刘肃肃, 余音. 复材非线性及渐进损伤的态型近场动力学模拟[J]. 浙江大学学报:工学版, 2016, 50(5):993-1000. LIU Su-su, YU Yin. State-based peridynamic modeling of nonlinear behavior and progressive damage of composites[J] Journal of Zhejiang University:Engineering Science, 2016, 50(5):993-1000.
[8] ZHOU X P, GU X B, WANG Y T. Numerical simulations of propagation, bifurcation and coalescence of cracks in rocks[J]. International Journal of Rock Mechanics & Mining Sciences, 2015, 80:241-254.
[9] WANG Y, ZHOU X, XU X. Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics[J]. Engineering Fracture Mechanics, 2016, 163:248-273.
[10] GERSTLE W, SAU N, SILLING S A. Peridynamic modeling of concrete structures[J]. Applied Mechanics and Materials, 2007, 237:1250-1258.
[11] GERSTLE W, SAU N, SAKHAVAND N. On peridynamic computational simulation of concrete structures[J]. Aci Special Publication, 2009, 265:245-264.
[12] HA Y D, BOBARU F. Characteristics of dynamic brittle fracture captured with peridynamics[J]. Engineering Fracture Mechanics, 2011, 78(6):1156-1168.
[13] KILIC B, MADENCI E. Structural stability and failure analysis using peridynamic theory[J]. International Journal of Non-linear Mechanics, 2009, 44:845-854.
[14] 沈峰, 章青, 黄丹,等. 基于近场动力学理论的混凝土轴拉破坏过程模拟[J]. 计算力学学报, 2013, 30(增1):79-83. SHEN Feng, ZHANG Qing, HUANG Dan, et al. Damage and failure process of concrete structure under uni-axialtension based on peridynamics modeling[J]. Chinese Journal of Computational Mechanics, 2013, 30(Suppl. 1):79-83.
[15] HUANG D, ZHANG Q, QIAO P Z. Damage and progressive failure of concrete structures using non-local peridynamic modeling[J]. Science China Technological Science, 2011, 54(3):591-596.
[16] HUANG D, LU G, QIAO P. An improved peridynamic approach for quasistatic elastic deformation and brittle fracture analysis[J]. International Journal of Mechanical Sciences, 2015, 94/95:111-122.
[17] SILLING S A, ASKARI E. A meshfree method based on the peridynamic model of solid mechanics[J]. Computters & Structures, 2005, 83(17/18):1526-1535.
[18] HUANG D, LU G, WANG C, et al. An extended peridynamic approach for deformation and fracture analysis[J]. Engineering Fracture Mechanics, 2015, 141:196-211.
[19] 顾鑫, 章青, 黄丹. 基于近场动力学方法的混凝土板侵彻问题研究[J]. 振动与冲击, 2016, 35(6):52-58. GU Xin, ZHANG Qing, HUANG Dan. Peridynamics used in solving penetration problem of concrete slabs[J]. Journal of Vibration and Shock, 2016, 35(6):52-58.
[20] HAERI H, SHAHRIAR K, MARJI M F, et al. Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks[J]. International Journal of Rock Mechanics & Mining Sciences, 2014, 67(4):20-28.
[21] 徐栋栋, 郑宏, 杨永涛,等. 多裂纹扩展的数值流形法[J]. 力学学报, 2015, 47(3):471-481. XU Dong-dong, ZHENG Hong, YANG Yong-tao, et al. Multiple crack propagation based on the numerical manifold method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3):471-481.
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