内聚单元模型在混凝土断裂数值模拟中的应用
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摘要
对于断裂的数值模拟一直是一个难点问题，无论在一般固体领域，还是在混凝土结构中。尤其是对于动态断裂问题，其数值模拟更是困难。新近得到广泛运用的内聚单元模型是专门为断裂数值计算而提出来的。内聚模型理论中，断裂认为是一个渐变过程——初始裂纹两侧的分离受到内聚力的阻挠，内聚力与张开量是由内聚关系确定的。内聚模型作为一个完全的断裂理论，不被任何材料特性、有限运动、非比例载荷、动力学或是试件的几何尺寸所限制。已证实此理论对复杂的断裂过程的模拟是有效的，包括：脆性材料的断裂、韧性材料的动态断裂和破碎、混凝土的动态Bazilian测试等等。
本文主要对内聚模型在混凝土断裂数值模拟中的应用做了一些讨论，并推导出了一种简单的二维六结点等参内聚单元，并用Fortran语言编写了含有内聚单元的有限元程序对混凝土切口梁的断裂过程进行了计算。计算结果表明，此方法对于混凝土材料是适用的。
Numerical simulation of concrete fracture is a challenging topic. Concrete crack has in important effect on concrete structure, so it is critical to the calculation of concrete crack properly, especially in dynamic problem. Cohesive element model is regarded as an effective tool to solve the fracture calculation. In the cohesive theory, fracture is regarded as a gradual process in which the separation of the incipient crack flanks is resisted by cohesive tractions. The relation between the cohesive tractions and the opening displacements is governed by a cohesive law. Cohesive models furnish a complete theory of fracture that is not limited by any consideration of material behavior, finite kinematics, non-proportional loading, dynamics, or the geometry of the specimen. The cohesive theory has proved effective in the simulation of complex fracture processes including: the fragmentation of brittle materials; dynamic fracture and fragmentation of ductile materials; and the dynamic Brazilian test for concrete.
In this paper the introduction of the use cohesive element in concrete structure is given, and a kind of 2-D isoperimetric cohesive element is deduced. The fracture process of concrete notch beam is calculated by Fortran programming. The result shows that the method is feasible.
本文主要对内聚模型在混凝土断裂数值模拟中的应用做了一些讨论，并推导出了一种简单的二维六结点等参内聚单元，并用Fortran语言编写了含有内聚单元的有限元程序对混凝土切口梁的断裂过程进行了计算。计算结果表明，此方法对于混凝土材料是适用的。
Numerical simulation of concrete fracture is a challenging topic. Concrete crack has in important effect on concrete structure, so it is critical to the calculation of concrete crack properly, especially in dynamic problem. Cohesive element model is regarded as an effective tool to solve the fracture calculation. In the cohesive theory, fracture is regarded as a gradual process in which the separation of the incipient crack flanks is resisted by cohesive tractions. The relation between the cohesive tractions and the opening displacements is governed by a cohesive law. Cohesive models furnish a complete theory of fracture that is not limited by any consideration of material behavior, finite kinematics, non-proportional loading, dynamics, or the geometry of the specimen. The cohesive theory has proved effective in the simulation of complex fracture processes including: the fragmentation of brittle materials; dynamic fracture and fragmentation of ductile materials; and the dynamic Brazilian test for concrete.
In this paper the introduction of the use cohesive element in concrete structure is given, and a kind of 2-D isoperimetric cohesive element is deduced. The fracture process of concrete notch beam is calculated by Fortran programming. The result shows that the method is feasible.
引文
1. Y. Li, K.T. Ramesh and E.S.C. Chin, Characterization of the dynamic fracture of metal-ceramic composites, Proceedings of the U.S. Army Symposium on Solid Mechanics.
2. Ruiz. G., Pandolfi. A., Ortiz, M. (2001) Three-dimensional cohesive modeling of dynamic mixed-mode fracture. Int. J. Numer. Meth. Eng. 52(1-2), 97-120
3. Camacho. G.T., Ortiz. M. (1996) Computational modeling of impact damage in brittle materials. Int. J. Solids and Structures. 33(20-22), 2899-2938
4. Ruiz. G., Ortiz. M., Pandolfi. A. (2000) Three dimensional finite-element simulation of the dynamic brazilian tests on concrete cylinders. Int. J. Numer. Meth. Eng. 45(7), 963-994
5．刘明杰，刘东．引信机构动态特性仿真与结构设计．探测与控制学报，Vol．24，No．2，Jun．2002．10-13．
6．国外引信及相关技术跟踪报导．二一二研究所情报资料中心组，2001．12[内部资料]
7．[美]陈惠发．土木工程材料的本构方程(第一卷)．华中科技大学出版社，2001
8．吕西林，金国芳，吴晓涵．钢筋混凝土结构非线性有限元理论与应用．同济大学出版社．1997
9. Ngo. D. Scordelis A. C. (1967) Finite Element Analysis of Reinforced Concrete Beams. Journal of the American Concrete Institute, March, 64(3):152-163
10. Scordelis A.C., Past, Present and Future Development, Finite Element Analysis of Reinforced Concrete Structures, ASCE, 1996
11．尹双增．断裂、损伤理论及应用．清华大学出版社，1992
12．朱伯芳．有限单元法原理及应用．中国水利水电出版社，1998
13. Hillerborg. A., Modeer. M. and Petersson. P. (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res. 6:773-782
14. Dugdale. D.S (1960) Yielding of steel sheets containing slits. J. Mech. Phys. Solids. 8: 100-104.
15. Barenblatt. G. (1962) The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7:55-129
16. Gurson. A.L. (1977) Continuum theories of ductile rupture by void nucleation and
growth: Part I-yield criteria and flow rules for porous ductile media. J. Eng. Mater. Tech. 99:2-15
17． Tvergaard. V. (1990) Material failure by void growth to coalescence, pages 83-151． Academic Press.
18． Needleman. A. (1987) A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54:525-531
19． De-Andre's A., Pe'rez. J.L., Ortiz. M. (1999) Elastic-plastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Int. J. Solids and Structures. 36(15) : 2231-2258
20． Schwalbe. K.H. and Cornec. A. (1994) Modeling crack growth using local process zones. Technical report, GKSS research center, Geesthacht
21． Needleman. A. (1990) An analysis of decohesion along an imperfect interface. International Journal of Fracture. 42: 21-40
22． J.H. Rose, J. Ferrante and J.R. Smith. (1981) Physical Review Letters 47: 675-678
23． Xu. X.P., Needleman. A. (1994) Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids. 42: 1397-1434
24． Scheider. I. (2001b) Simulation of cup-cone fracture in round bars using the cohesive zone model. In First M.I.T. conference on Computational Fluid and Solid Mechanics, pages 460-462
25． Ortiz. M., Pandolfi. A. (1999) A class of cohesive elements for the simulation of three-dimensional crack propagation. Int. J. Numer. Meth. Eng. 44: 1267-1282
26． Tvergaard. V. and Hutchinson. J.W (1993) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J. Mech. Phys. Solids 40: 1377-1892
27． 徐次达，华伯浩．固体力学有限元理论、方法及程序．水利电力出版社，1983
28． 王勖成，邵敏．有限单元法基本原理和数值方法(第二版)．清华大学出版社，1997
29． A. Pandolfi, P. Krysl, M. Ortiz. (1999) Finite element simulation of ring expansion and fragmentation: the capturing of length and timescales through cohesive models of fracture. International Journal of Fracture 95: 279-297
30． Finot. M., She. Y.L., Needleman. A. and Suresh. S. (1994) Micro-mechanical modeling of
reinforcement fracture in plastic-reinforcement metal-matrix composites.Metall. Trans. 254: 2403-2420
31． 周储伟，杨卫，方岱宁．内聚力界面单元与复合材料的界面损伤分析．力学学报．1999． 3(3)
32． Carlos. G. Davlia, Pedro P. Camanho. (2001) Decohesion Elements using Two and Three-Parameter Mixed-Mode Criteria. America Helicopter Society Conference.
33． E.A. Repetto, R. Radovitzky, M. Ortiz. (2000) Finite element simulation of dynamic fracture and fragmentation of glass rods . Comput. Methods Appl. Mech. Engrg. 183: 3-14
34． O.Nguyen, E.A. Repetto, M. Ortiz., R.A. Radovitzky (2001) A cohesive model of fatigue crack growth. InternationalJournal of Fracture. 110: 351-369
35． Sushovan Roychowdhury, Yamuna Das Arun Roy, Robert H., Dodds Jr. (2002) Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-Dsurface cohesive element. Engineering Fracture Mechanics. 69: 983-1002
36 Molinari. J.F., Ortiz. M. (2002) Three-dimensional adaptive meshing by subdivision and edge-collapse in finite-deformation dynamic-plasticity problems with application to adiabatic shear banding. Int. J. Numer. Meth. Eng. 53(5) : 1101-1126
37． Pandolfi. A., Ortiz. M. (1998) Solid modeling aspects of three-dimensional fragmentation. Eng. with Comput.14 (4) : 287-308
38 A. Pandolfi, M. Ortiz. (2002) An efficient adaptive procedure for three-dimensional fragmentation simulation. Engineering with Computer. 18: 148-159
2. Ruiz. G., Pandolfi. A., Ortiz, M. (2001) Three-dimensional cohesive modeling of dynamic mixed-mode fracture. Int. J. Numer. Meth. Eng. 52(1-2), 97-120
3. Camacho. G.T., Ortiz. M. (1996) Computational modeling of impact damage in brittle materials. Int. J. Solids and Structures. 33(20-22), 2899-2938
4. Ruiz. G., Ortiz. M., Pandolfi. A. (2000) Three dimensional finite-element simulation of the dynamic brazilian tests on concrete cylinders. Int. J. Numer. Meth. Eng. 45(7), 963-994
5．刘明杰，刘东．引信机构动态特性仿真与结构设计．探测与控制学报，Vol．24，No．2，Jun．2002．10-13．
6．国外引信及相关技术跟踪报导．二一二研究所情报资料中心组，2001．12[内部资料]
7．[美]陈惠发．土木工程材料的本构方程(第一卷)．华中科技大学出版社，2001
8．吕西林，金国芳，吴晓涵．钢筋混凝土结构非线性有限元理论与应用．同济大学出版社．1997
9. Ngo. D. Scordelis A. C. (1967) Finite Element Analysis of Reinforced Concrete Beams. Journal of the American Concrete Institute, March, 64(3):152-163
10. Scordelis A.C., Past, Present and Future Development, Finite Element Analysis of Reinforced Concrete Structures, ASCE, 1996
11．尹双增．断裂、损伤理论及应用．清华大学出版社，1992
12．朱伯芳．有限单元法原理及应用．中国水利水电出版社，1998
13. Hillerborg. A., Modeer. M. and Petersson. P. (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res. 6:773-782
14. Dugdale. D.S (1960) Yielding of steel sheets containing slits. J. Mech. Phys. Solids. 8: 100-104.
15. Barenblatt. G. (1962) The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7:55-129
16. Gurson. A.L. (1977) Continuum theories of ductile rupture by void nucleation and
growth: Part I-yield criteria and flow rules for porous ductile media. J. Eng. Mater. Tech. 99:2-15
17． Tvergaard. V. (1990) Material failure by void growth to coalescence, pages 83-151． Academic Press.
18． Needleman. A. (1987) A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54:525-531
19． De-Andre's A., Pe'rez. J.L., Ortiz. M. (1999) Elastic-plastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Int. J. Solids and Structures. 36(15) : 2231-2258
20． Schwalbe. K.H. and Cornec. A. (1994) Modeling crack growth using local process zones. Technical report, GKSS research center, Geesthacht
21． Needleman. A. (1990) An analysis of decohesion along an imperfect interface. International Journal of Fracture. 42: 21-40
22． J.H. Rose, J. Ferrante and J.R. Smith. (1981) Physical Review Letters 47: 675-678
23． Xu. X.P., Needleman. A. (1994) Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids. 42: 1397-1434
24． Scheider. I. (2001b) Simulation of cup-cone fracture in round bars using the cohesive zone model. In First M.I.T. conference on Computational Fluid and Solid Mechanics, pages 460-462
25． Ortiz. M., Pandolfi. A. (1999) A class of cohesive elements for the simulation of three-dimensional crack propagation. Int. J. Numer. Meth. Eng. 44: 1267-1282
26． Tvergaard. V. and Hutchinson. J.W (1993) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J. Mech. Phys. Solids 40: 1377-1892
27． 徐次达，华伯浩．固体力学有限元理论、方法及程序．水利电力出版社，1983
28． 王勖成，邵敏．有限单元法基本原理和数值方法(第二版)．清华大学出版社，1997
29． A. Pandolfi, P. Krysl, M. Ortiz. (1999) Finite element simulation of ring expansion and fragmentation: the capturing of length and timescales through cohesive models of fracture. International Journal of Fracture 95: 279-297
30． Finot. M., She. Y.L., Needleman. A. and Suresh. S. (1994) Micro-mechanical modeling of
reinforcement fracture in plastic-reinforcement metal-matrix composites.Metall. Trans. 254: 2403-2420
31． 周储伟，杨卫，方岱宁．内聚力界面单元与复合材料的界面损伤分析．力学学报．1999． 3(3)
32． Carlos. G. Davlia, Pedro P. Camanho. (2001) Decohesion Elements using Two and Three-Parameter Mixed-Mode Criteria. America Helicopter Society Conference.
33． E.A. Repetto, R. Radovitzky, M. Ortiz. (2000) Finite element simulation of dynamic fracture and fragmentation of glass rods . Comput. Methods Appl. Mech. Engrg. 183: 3-14
34． O.Nguyen, E.A. Repetto, M. Ortiz., R.A. Radovitzky (2001) A cohesive model of fatigue crack growth. InternationalJournal of Fracture. 110: 351-369
35． Sushovan Roychowdhury, Yamuna Das Arun Roy, Robert H., Dodds Jr. (2002) Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-Dsurface cohesive element. Engineering Fracture Mechanics. 69: 983-1002
36 Molinari. J.F., Ortiz. M. (2002) Three-dimensional adaptive meshing by subdivision and edge-collapse in finite-deformation dynamic-plasticity problems with application to adiabatic shear banding. Int. J. Numer. Meth. Eng. 53(5) : 1101-1126
37． Pandolfi. A., Ortiz. M. (1998) Solid modeling aspects of three-dimensional fragmentation. Eng. with Comput.14 (4) : 287-308
38 A. Pandolfi, M. Ortiz. (2002) An efficient adaptive procedure for three-dimensional fragmentation simulation. Engineering with Computer. 18: 148-159
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