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摘要:
在采用UH模型的用户材料子程序（UMAT）进行有限元计算过程中时常会出现局部单元破坏的情况，主要包括拉裂和剪坏，这种破坏应力状态的存在不仅会使得计算结果不合理，也会降低有限元计算的稳定性。针对采用UH模型UMAT进行有限元计算时遇到的局部单元破坏问题，根据一定的假设条件，并结合不同坐标系下的应力变换关系，推导得到适用于UH模型的三维问题单元破坏修正公式；采用FORTRAN语言编写出相应的子程序，将其嵌入UH模型UMAT中，以消除采用UH模型进行有限元计算时出现的不合理的破坏应力状态，提高UH模型UMAT有限元计算的稳定性，并通过有限元模拟基坑开挖的例子验证本文所提的单元破坏修正方法的有效性和合理性。
Abstract:The problem of some elements' damage often appears when finite element calculation of using UH model UMAT is conducted, including tension failure and shear failure. The failure stress state not only makes the results unreasonable, but also reduces the stability of calculation. To solve the problem generated by unreasonable failure stress state when the UH model's UMAT is used to conduct finite element analysis, based on certain assumptions and combined with stress transformation relationship under different coordinates, three-dimensional element failure correction formulas for UH model can be elicited. Then FORTRAN language is used to write the subroutine of element failure correction, and it is embedded in the UH model's UMAT to eliminate the unreasonable failure stress state and improve the stability of finite element calculation. Finally, an example of foundation pit excavation is used to verify the validity and rationality of this method.
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Key words:
- UH model /
- UMAT /
- finite element /
- tension failure /
- shear failure /
- failure correction
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图 1 UH模型的当前屈服面与参考屈服面
Figure 1. Current yield surface and referential yield surface of UH model
图 12 有无破坏修正的土体的竖向位移等值云图
Figure 12. Vertical displacement contour of soils with and without failure correction
表 1 新旧坐标轴之间的方向余弦
Table 1. Direction cosine between new and old coordinate
坐标轴 x y z x′ l1 m1 n1 y′ l2 m2 n2 z′ l3 m3 n3 
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表 2 UH模型参数取值
Table 2. Parameter value of UH model
参数 M ν κ λ e0 N c/kPa 数值 0.984 0.3 0.016 0.09 0.6 1.15 10
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表 3 破坏修正前后计算结果对比
Table 3. Comparison of calculation results before and after failure correction
变量 1 244号单元第1积分点 18号单元第4积分点 修正前 修正后 修正前 修正后 
32.53 32.53 42.11 42.11 
7.39 23.97 5.07 23.93 
-14.16 21.44 -7.47 21.44 σx/kPa -11.16 3.51 -15.61 2.86 σy/kPa -35.600 0.007 -28.910 0 σz/kPa 8.19 10.10 19.92 20.30 τxz/kPa -8.03 -2.74 -5.24 -2.57 
4.714 0.387 3.373 0.670 
1.908 1.908 1.801 1.801 
-0.223 29.290 -0.444 10.830
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