粘性离散裂缝模型及其对混凝土尺寸效应的模拟
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摘要
比例边界有限元法是一种新颖的半解析方法，它集成了边界元法和有限元法各自的优点：和边界元法一样，这种方法仅需离散计算域的边界；但它不需要基本解，因此比边界元有更宽广的应用范围。此外这种方法还具有自身独特的优势，如它的位移场和应力场在径向是解析的，这使得裂缝尖端的应力强度因子可以从其定义直接推导出来，不需要使用传统有限元法和边界元法必须的网格加密或特殊奇异单元。
本文运用比例边界有限元法对混凝土材料中粘性裂缝的扩展进行全自动模拟。首先将计算域划分成若干子域，子域的个数，尺寸和几何形状可以根据需要灵活确定。由于不需要进行网格加密和使用奇异单元，网格重分程序变得和边界元法中一样简单，仅需要一些很少的网格改变。本文在前人发展的以线弹性断裂力学为基础的网格重分程序上自动增加非线性界面单元。采用粘性裂缝模型来模拟断裂过程区。非线性方程通过局部弧长法进行求解。模型假定当张开应力强度因子K_I≥0的时候，裂缝扩展，扩展的方向由线弹性断裂力学准则决定。对裂缝开展过程中裂缝过程区的演化进行了精细模拟。作为算例，对混凝土梁的尺寸效应进行了详细模拟和分析。
算例结果表明，比例边界有限元法仅使用很少的自由度，就能够对混凝土粘性裂缝扩展进行较为准确的模拟，所得混凝土梁弯曲抗拉强度的尺寸效应的结果和实验及理论结果吻合较好。由于其半解析的性质，这种方法可以采用同一个初始网格对尺寸变化很大的相似混凝土梁进行模拟，这大大减少了前处理的工作强度，因此特别适合对混凝土强度的尺寸效应进行模拟。
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique, combining the advantages of the finite element method and the boundary element method with unique properties of its own. Like the boundary element method, it discretises domain boundaries only so reduces the modelled dimentions by one; but it does not need fundamental solutions and thus has wider applicabilities. One of the most important advangtages of the SBFEM is that its displacement and stress solutions are analytical in the radial direction. This allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatments, such as refining the crack-tip mesh or using singular elements(needed in the traditional finite element method and boundary element method), is necessary.
This study applies the SBFEM to fully-automatically model cohesive crack growth in quasi-brittle materials such as concrete. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised, a remeshing procedure as simple as in the boundary element method was developed with minimum mesh changes whereas the generality and flexibility of the finite element method is well maintained. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. Cohesive/fictitious crack model is used to simulate the fracture process zone. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K_1≥0 in the direction determined by LEFM criteria. The evolution of the FPZ is predicted by the present method.
Comparison of the numerical results with those obtained from experiments and analytical studies shows that the SBFEM is able to accurately model the cohesive crack propagation and size effect in concrete beams using a small number of degrees
of freedom. In particular, it can model similar concrete beams with a wide range of dimensions using the same initial mesh. This means tremendous reduction in pre-process and data preparation, which makes the SBFEM very suitable for modeling size effect in concrete beams.
本文运用比例边界有限元法对混凝土材料中粘性裂缝的扩展进行全自动模拟。首先将计算域划分成若干子域，子域的个数，尺寸和几何形状可以根据需要灵活确定。由于不需要进行网格加密和使用奇异单元，网格重分程序变得和边界元法中一样简单，仅需要一些很少的网格改变。本文在前人发展的以线弹性断裂力学为基础的网格重分程序上自动增加非线性界面单元。采用粘性裂缝模型来模拟断裂过程区。非线性方程通过局部弧长法进行求解。模型假定当张开应力强度因子K_I≥0的时候，裂缝扩展，扩展的方向由线弹性断裂力学准则决定。对裂缝开展过程中裂缝过程区的演化进行了精细模拟。作为算例，对混凝土梁的尺寸效应进行了详细模拟和分析。
算例结果表明，比例边界有限元法仅使用很少的自由度，就能够对混凝土粘性裂缝扩展进行较为准确的模拟，所得混凝土梁弯曲抗拉强度的尺寸效应的结果和实验及理论结果吻合较好。由于其半解析的性质，这种方法可以采用同一个初始网格对尺寸变化很大的相似混凝土梁进行模拟，这大大减少了前处理的工作强度，因此特别适合对混凝土强度的尺寸效应进行模拟。
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique, combining the advantages of the finite element method and the boundary element method with unique properties of its own. Like the boundary element method, it discretises domain boundaries only so reduces the modelled dimentions by one; but it does not need fundamental solutions and thus has wider applicabilities. One of the most important advangtages of the SBFEM is that its displacement and stress solutions are analytical in the radial direction. This allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatments, such as refining the crack-tip mesh or using singular elements(needed in the traditional finite element method and boundary element method), is necessary.
This study applies the SBFEM to fully-automatically model cohesive crack growth in quasi-brittle materials such as concrete. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised, a remeshing procedure as simple as in the boundary element method was developed with minimum mesh changes whereas the generality and flexibility of the finite element method is well maintained. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. Cohesive/fictitious crack model is used to simulate the fracture process zone. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K_1≥0 in the direction determined by LEFM criteria. The evolution of the FPZ is predicted by the present method.
Comparison of the numerical results with those obtained from experiments and analytical studies shows that the SBFEM is able to accurately model the cohesive crack propagation and size effect in concrete beams using a small number of degrees
of freedom. In particular, it can model similar concrete beams with a wide range of dimensions using the same initial mesh. This means tremendous reduction in pre-process and data preparation, which makes the SBFEM very suitable for modeling size effect in concrete beams.
引文
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[3] B.Cotterel. The past, present, and future of fracture mechanics [J] .Engineering Facture Mechanics 69 (2002):533-553.
[4] 方韬，龚顺风，金伟良．混凝土结构破坏过程的离散单元法模拟[J]．浙江大学学报(工学版)2004，38(7)：921-925．
[5] 周维垣，黄岩松，林鹏．三维无单元伽辽金法及其在拱坝分析中的应用[J]．水利学报2005，36(6)：644-649．
[6] Lou Luliang, Zeng Pan.MESHLESS METHOD FOR 2D MIXED. MODE CRACK PROPAGATION BASED ON VORONOI CELL[J]. ACTA MECHANICA SoLIDA SINICA 16(2003),231-239
[7] Ingrafea A R, Blandford G, andLigget J A. Automatic modeling of mixed-mode fatigue and quasi—static crack propagation using the boundary element method[A]. 14th Natl Symp on Fracture[C], 1987,ASTM STP 791:1407-1426
[8] Portela A, Aliabadi M H and Rooke D P. Dual boundary element in—crernental analysis of crack propagation[J]. Int J Cornput Struct, 1993.46:237～247
[9] 邓建刚，蒋和洋，黎在良，闫维明，三维裂纹扩展轨迹的边界元数值模拟[J]．应用力学学报2003，20(2)：49-53
[10] 王水林，葛修润，流形元方法在模拟裂纹扩展中的应用[J]．岩土力学与工程学报1997，16(5)：405-410
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