裂纹-夹杂问题分析的本征计算模型及其数值模拟

郭钊; 任晓丹; 和东宏

doi:10.21656/1000-0887.450134

裂纹-夹杂问题分析的本征计算模型及其数值模拟

doi: 10.21656/1000-0887.450134

1. 九江学院建筑工程与规划学院，江西九江 332005;
2. 同济大学土木工程学院，上海 200092;
3. 滇西应用技术大学建筑工程学院，云南大理 67100

基金项目:

国家自然科学基金（12162015；12362018）；江西省自然科学基金（面上项目）（20202BABL201015）

详细信息

作者简介:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

通讯作者:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

中图分类号: O341
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出版历程
- 收稿日期: 2024-05-11
- 修回日期: 2024-07-02
- 网络出版日期: 2025-04-02
- 刊出日期: 2025-03-01

Numerical Modeling for the Analysis of Crack-Inclusion Problems by the Eigen Iterative Computational Model

1. College of Architecture Engineering and Planning, Jiujiang University, Jiujiang, Jiangxi 332005, P.R.China;
2. College of Civil Engineering, Tongji University, Shanghai 200092, P.R.China;
3. College of Civil Engineering and Architecture, West Yunnan University of Applied Sciences, Dali, Yunnan 671006, P.R.China

Funds:

The National Science Foundation of China(12162015；12362018)

摘要

摘要: 针对固体材料含有“裂纹夹杂”的数值模拟问题，将Eshelby本征应变和等效夹杂替换理论引入边界积分方程中，建立了本征裂纹张开位移（crack opening displacement, COD）和本征应变边界积分方程的计算模型及数值实现，以解决“裂纹夹杂”的相互作用机制.在一定条件下，异性夹杂可以作为一般的夹杂问题处理，物理上可令夹杂的弹性模量为零，则该夹杂就“退化”为孔洞；同时，在几何上可令其最小尺寸方向上的尺寸为零，即可进一步“退化”为裂纹，因而裂纹可被认为是弹性模量为零的一种特殊夹杂.采用边界积分方程的离散形式对裂纹和夹杂问题进行了数值验证，其中裂纹和夹杂的边界分别采用Gauss配点法和边界点法进行离散，进行了应力分析，研究了裂纹与夹杂的相互作用.数值算例验证了本征计算模型处理“裂纹夹杂”问题的正确性和方法的可行性，也表现出较高的计算精度，为该计算模型的大规模数值分析奠定了理论基础.
- “裂纹-夹杂”问题 /
- 本征裂纹张开位移 /
- 本征应变 /
- 边界积分方程 /
- 数值模拟
Abstract: For the numerical modeling of solid materials containing crack-inclusions, the theory of Eshelby’s eigenstrain and equivalent inclusion was incorporated into the boundary integral equations (BIEs). A computation model and an iterative algorithm for the eigen crack opening displacement (COD) and eigenstrain BIEs to address the interaction of crack-inclusions were proposed. Under certain conditions, anisotropic inclusions may be considered as general inclusions. When the elastic modulus of the inclusion is set to zero, the inclusion will degenerate into a hole, and geometrically, with its minimum dimension reduced to zero further it will degenerate into a crack. Thereby, a crack was classified as a special type of inclusion with zero elastic modulus. The discrete form of the boundary integral equation was utilized for the numerical validation of cracks and inclusions, with their boundaries discretized with Gaussian integration points and the boundary point methods, respectively, to conduct stress analysis and investigate the interaction between crack-inclusions. Numerical examples confirm the correctness and feasibility of the eigen iterative model in modeling crack-inclusion problems, demonstrating its high computation accuracy, and providing the theoretical foundation for future large-scale numerical analysis with this computation model.
- crack-inclusion problem /
- eigen COD /
- eigen strain /
- boundary integral equation /
- numerical modeling

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参考文献(29)

[2]WU J Y, XU S L. An augmented multicrack elastoplastic damage model for tensile cracking[J].International Journal of Solids and Structures,2011,48(18): 2511-2528.

DOLADO J S, VAN BREUGEL K. Recent advances in modeling for cementitious materials[J].Cement and Concrete Research,2011,41(7): 711-726.

[3]XIAO H T, YUE Z Q. A three-dimensional displacement discontinuity method for crack problems in layered rocks[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(3): 412-420.

[4]ZHOU X P, LI X H. Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects[J].Theoretical and Applied Fracture Mechanics,2009,52(3): 140-145.

[5]CHMELIK F, TRNIK A, IGOR S, et al. Creation of microcracks in porcelain during firing[J].Journal of the European Ceramic Society,2011,31(13): 2205-2209.

[6]PINEAU A, TANGUY B. Advances in cleavage fracture modelling in steels: micromechanical, numerical and multiscale aspects[J].Comptes Rendus Physique,2010,11(3/4): 316-325.

[7]SOBELMAN O S, GIBELING J C, STOVER S M, et al. Do microcracks decrease or increase fatigue resistance in cortical bone?[J].Journal of Biomechanics,2004,37(9): 1295-1303.

[8]SHI D L, FENG X Q, JIANG H, et al. Multiscale analysis of fracture of carbon nanotubes embedded in composites[J].International Journal of Fracture,2005,134(3): 369-386.

[9]张国瑞. 有限元法[M]. 北京: 机械工业出版社, 1991. (ZHANG Guorui.Finite Element Method[M]. Beijing: China Machine Press, 1991. (in Chinese))

[10]杨庆生, 杨卫. 断裂过程的有限元模拟[J]. 计算力学学报, 1997,14(4): 407-412. (YANG Qingsheng, YANG wei. Finite element simulation of fracture process[J].Chinese Journal of Computational Mechanics,1997,14(4): 407-412. (in Chinese))

[11]ALIABADI M H. Boundary element formulations in fracture mechanics[J].Applied Mechanics Reviews,1997,50(2): 83-96.

[12]ESHELBY J D. The determination of the elastic field of an ellipsoidal inclusion, and related problems[J].Proceedings of the Royal Society of London (Series A): Mathematical and Physical Sciences,1957,241(1226): 376-396.

[13]ESHELBY J D. The elastic field outside an ellipsoidal inclusion[J].Proceedings of the Royal Society of London (Series A): Mathematical and Physical Sciences,1959,252(1271): 561-569.

[14]DONG C Y, CHEUNG Y K, LO S H. A regularized domain integral formulation for inclusion problems of various shapes by equivalent inclusion method[J].Computer Methods in Applied Mechanics and Engineering,2002,191(31): 3411-3421.

[15]DONG C Y, LEE K. Boundary element analysis of infinite anisotropic elastic medium containing inclusions and cracks[J].Engineering Analysis With Boundary Elements,2005,29(6): 562-569.

[16]DONG C Y. Effective elastic properties of doubly periodic array of inclusions of various shapes by the boundary element method[J].International Journal of Solids and Structures,2006,43(25/26): 7919-7938.

[17]LIU Y J, NISHIMURA N, OTANI Y, et al. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model[J].Journal of Applied Mechanics,2005,72(1): 115-128.

[18]马杭, 夏利伟, 秦庆华. 短纤维复合材料的本征应变边界积分方程计算模型[J]. 应用数学和力学, 2008,29(6): 687-695. (MA Hang, XIA Liwei, QIN Qinghua. Computational model for short-fiber composites with eigen-strain formulation of boundary integral equations[J].Applied Mathematics and Mechanics,2008,29(6): 687-695. (in Chinese))

[19]MA H, YAN C, QIN Q. Eigenstrain formulation of boundary integral equations for modeling particle-reinforced composites[J].Engineering Analysis With Boundary Elements,2008,33: 410-419.

[20]MA H, FANG J B, QIN Q H. Simulation of ellipsoidal particle-reinforced materials with eigenstrain formulation of 3D BIE[J].Advances in Engineering Software,2011,42(10): 750-759.

[21]马杭, 郭钊, 秦庆华. 二维多项式本征应变边界积分方程及其数值验证[J]. 应用数学和力学, 2011,32(5): 522-532. (MA Hang, GUO Zhao, QIN Qinghua. Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification[J].Applied Mathematics and Mechanics,2011,32(5): 522-532. (in Chinese))

[22]GUO Z, MA H. Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation[J].Journal of Shanghai University (English Edition), 2011,15(3): 173-179.

[23]郭钊, 郭子涛, 易玲艳. 多裂纹问题计算分析的本征COD边界积分方程方法[J]. 应用数学和力学, 2019,40(2): 200-209. (GUO Zhao, GUO Zitao, YI Lingyan. Analysis of multicrack problems with eigen COD boundary integral equations[J].Applied Mathematics and Mechanics,2019,40(2): 200-209. (in Chinese))

[24]中国航空研究院. 应力强度因子手册[M]. 北京: 科学出版社, 1981. (Chinese Aeronautical Establishment.Handbook of Stress Intensity Factor[M]. Beijing: Science Press, 1981. (in Chinese))

[25]ERDOGAN F, GUPTA G D, RATWANI M. Interaction between a circular inclusion and an arbitrarily oriented crack[J].Journal of Applied Mechanics,1974,41(4): 1007-1013.

[26]TANG R, WANG Y. On the problem of crack system with an elliptic hole[J].Acta Mechanica Sinica,1986,2(1): 47-57.

[27]HAN X L, WANG Z Q, Elastic fields of interacting elliptic inhomogeneities[J].International Journal of Solids and Structures,1999,36: 4523-4541

[28]MA H, QIN Q H. Solving potential problems by a boundary-type meshless method: the boundary point method based on BIE[J].Engineering Analysis with Boundary Elements,2007,31(9): 749-761.

[29]马杭, 周鹃. 基于二次移动单元的边界点法解弹性力学问题[J]. 上海大学学报(自然科学版), 2009,15(6): 581-585. (MA Hang, ZHOU Juan. Boundary point method based on quadratic moving elements for elasticity[J].Journal of Shanghai University (Natural Science Edition), 2009,15(6): 581-585. (in Chinese))

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裂纹-夹杂问题分析的本征计算模型及其数值模拟

doi: 10.21656/1000-0887.450134

作者简介:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

通讯作者:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

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Numerical Modeling for the Analysis of Crack-Inclusion Problems by the Eigen Iterative Computational Model

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留言板

裂纹-夹杂问题分析的本征计算模型及其数值模拟

doi: 10.21656/1000-0887.450134

作者简介: 郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

通讯作者: 郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

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出版历程

Numerical Modeling for the Analysis of Crack-Inclusion Problems by the Eigen Iterative Computational Model

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出版历程

目录

作者简介:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.

通讯作者:
郭钊（1986—），男，教授，博士，硕士生导师，江西省赣鄱俊才高校青年领军人才（江西省青年井冈学者）（通讯作者. E-mail: guozhao@shu.edu.cn）.