Dynamic damage constitutive model of sandstone based on component combination theory
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摘要: 采用分离式霍普金森压杆（SHPB）系统，对砂岩进行不同速度下的冲击试验，得到砂岩的应变率效应特征以及典型的动态本构曲线。该曲线分为近似线弹性阶段、塑性阶段、塑性增强阶段和正向卸载阶段。通过组合模型的方法，构建了砂岩含损伤的动态本构模型，借助LS-DYNA软件中的用户材料子程序UMAT接口实现对本构模型的二次开发，并对砂岩在冲击速度为7.5、9.5、11.5和13.5 m/s 4种情况下的SHPB动态冲击压缩试验进行模拟。结果表明：所构建的模型可以很好地描述砂岩的应变率效应和应力-应变曲线弹性段，并且动态峰值强度、最大应变均与试验结果一致，应变率、峰值强度、最大应变与试验结果的相对误差不超过10%。所构建的砂岩动态本构模型能够准确地描述砂岩在冲击作用下的动态力学特性。Abstract: In this study, using a split Hopkinson pressure bar (SHPB) system, we conducted the impact tests of sandstone at different impact velocities to collect the characteristics of the strain rate effect and obtained the typical dynamic constitutive curve of sandstone. The curve can be divided into an approximately linear elastic stage, a plastic stage, a plastic enhancement stage and a forward unloading stage. We constructed the dynamic damage constitutive model of sandstone adopting the combination model, and utilized the user subroutine UMAT interface of LS-DYNA to achieve the secondary development of the constitutive model, which was then used to simulate the SHPB dynamic impact compression tests of sandstone at four impact rates of 7.5, 9.5, 11.5 and 13.5 m/s. The calculation results showed that the as-constructed model gave a good description of the effect of the strain rate and the elastic stage of the stress-strain curve of sandstone. Moreover, the dynamic peak strength and maximum strain were in good agreement with the test results, and the relative errors of the strain rate, peak strength, maximum strain were less than 10%, thus indicating that the as-constructed dynamic constitutive model can accurately describe the dynamic mechanical properties of sandstone under impact.
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Key words:
- rock dynamic mechanics /
- split Hopkinson pressure bar /
- constitutive model /
- damage
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图 1 砂岩在不同冲击速度下的破坏形态
Figure 1. Failure patterns of sandstone at different impact velocities
图 2 不同应变率下砂岩的本构曲线
Figure 2. Stress-strain curves of sandstone at different strain rates
图 5 自定义本构模型在LS-DYNA中的计算流程
Figure 5. Calculation flow of user-defined constitutive model in LS-DYNA
图 6 不同冲击速度下试验与数值模拟结果对比
Figure 6. Comparison of tests and simulations at different impact velocities
表 1 砂岩动态力学特性的试验与模拟结果
Table 1. Tests and simulations of dynamic mechanical characteristics of sandstone
方法 v/(m·s-1) ${\dot{\varepsilon }}$/s-1 σd, max/MPa εmax/10-3 模拟 7.5 55.53 48.08 1.820 模拟 9.5 64.06 63.18 2.170 模拟 11.5 81.36 88.94 3.920 模拟 13.5 85.25 97.14 6.080 试验 7.5 52.39 50.93 2.000 试验 9.5 64.71 63.32 2.260 试验 11.5 78.23 95.87 3.900 试验 13.5 90.69 102.74 6.017 
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