3D Numerical Simulation of Concrete Cracking Based on Specified Stress Method
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摘要: 基于指定应力方法，根据线弹性理论推导出了一种新的混凝土开裂的空间有限元列式，根据该有限元公式编制了相应的C++计算程序. 通过3个算例，将该文算法与理论结果以及ABAQUS中XFEM计算结果进行对比，验证了该文开裂算法的正确性. 与常规开裂算法相比，该文开裂算法开裂积分点的应力一旦指定为零(开裂状态)，在后续计算中将不会出现非零，不需要迭代过程去调整为零，大大减少了迭代次数和每次迭代过程中需要处理的数据量；相较于ABAQUS中的XFEM算法只能使用一阶单元，本文开裂算法可以使用二阶单元进行开裂计算，在其他计算环境相同的情况下对开裂区域和开裂状态的判断更准确，这为商业有限元软件采用二阶单元进行更精细的开裂计算提供了一种新的途径和算法.Abstract: Based on the specified stress method, a new spatial finite element formulation for concrete cracking was derived according to the linear elasticity theory. This formulation was used to create a calculation program with the C++ language. The accuracy of the proposed cracking algorithm was validated through 3 numerical examples, where the theoretical results were compared with the ABAQUS XFEM calculations. Beyond conventional cracking algorithms, the proposed cracking algorithm has the advantage that once the stress at the cracking integration point is specified as zero (in the cracking state), it will remain zero in subsequent calculations. There is no need for an iterative process to adjust it to zero, which means significant reduction of the number of iterations and the amount of data processing required in each iteration. In comparison to the ABAQUS XFEM algorithm, which is limited to the 1st-order elements, the proposed cracking algorithm can utilize the 2nd-order elements for crack calculation, and allows for a more accurate determination of the cracked regions and states under the same computational conditions. This work provides a new approach and algorithm for commercial finite element software to conduct more refined crack calculations with the 2nd-order elements.
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Key words:
- specified stress methods /
- finite element /
- concrete cracking /
- 3D numerical simulation
edited-byedited-by1) （我刊编委易志坚来稿） -
图 1 基于指定应力方法的混凝土开裂计算流程
Figure 1. The calculation flowchart for concrete cracking based on the specified stress method
图 2 受轴向拉伸载荷的矩形悬臂梁(单位：mm)
Figure 2. The rectangular cantilever beam subject to axial tensile load (unit: mm)
图 5 悬臂T梁迭代20次裂纹扩展状态
Figure 5. The crack propagation state of the cantilever T-beam after 20 iterations
图 6 悬臂T梁迭代30次裂纹扩展状态
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 6. The crack propagation state of the cantilever T-beam after 30 iterations
图 7 预制裂纹简支梁示意图(单位：mm)
Figure 7. Schematic diagram of the precracked simply supported beams (unit: mm)
图 8 预制裂纹简支梁STATUSXFEM云图(u=－0.000 4 m)
Figure 8. The STATUSXFEM nephogram of the precracked simply supported beam(u=－0.000 4 m)
图 9 预制裂纹简支梁STATUSXFEM云图(u=－0.004 m)
Figure 9. The STATUSXFEM nephogram of the precracked simply supported beam(u=－0.004 m)
图 10 预制裂纹简支梁裂纹扩展状态(u=－0.000 4 m)
Figure 10. The crack propagation state of the precracked simply supported beams(u=－0.000 4 m)
图 11 预制裂纹简支梁裂纹扩展状态(u=－0.004 m)
Figure 11. The crack propagation state of the precracked simply supported beams(u=－0.004 m)
表 1 有限元位移计算结果对比
Table 1. Comparison of calculation results of finite element displacements
№. of node ABAQUS (1 element) ABAQUS (2 elements) ABAQUS (20 elements) the present (1 element) U2 U3 U2 U3 U2 U3 U2 U3 1 -3.60E-5 -6.95E-20 -3.60E-5 -3.22E-18 -3.60E-5 -1.92E-17 -3.60E-5 -1.62E-18 2 -7.45E-19 -2.43E-18 -3.05E-20 -1.61E-18 -2.03E-17 -1.99E-17 9.83E-19 8.27E-19 3 -3.60E-5 2.70E-5 -3.60E-5 2.70E-5 -3.60E-5 2.70E-5 -3.60E-5 2.70E-5 4 9.20E-19 2.70E-5 -1.12E-18 2.70E-5 -2.03E-17 2.70E-5 -9.23E-19 2.70E-5 
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表 2 积分点的强度及其开裂位移荷载
Table 2. The strengths of the integral points and the correponding cracking displacement loads
№. strength ft/Pa cracking displacement load uc/m 6 2.14E6 7.99E-5 4 2.29E6 8.53E-5 2 2.33E6 8.71E-5 0 2.48E6 9.25E-5 7 3.10E6 1.16E-4 5 3.25E6 1.21E-4 3 3.30E6 1.23E-4 1 3.44E6 1.28E-4
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表 3 4种荷载工况下的开裂积分点个数及裂纹扩展路径
Table 3. The numbers of crack integral points and crack propagation paths four load conditions
displacement load u/m 7.90E-5 8.00E-5 1.00E-4 1.30E-4 number of crack integral points 0 1 4 8 crack propagation path - 6 6→4→2→0 6→4→2→0→7→5→3→1
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