Influence of shear-enhanced compaction and strain-rate effects on the equation of state for concrete-like materials
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摘要: 为研究爆炸冲击荷载作用下剪切增强效应和应变率效应对混凝土类材料状态方程的影响，基于水泥砂浆静水压缩和平板撞击两类状态方程行为实验，利用Kong-Fang混凝土类材料流体弹塑性模型和LS-DYNA中光滑粒子伽辽金（smoothed particle Galerkin, SPG）算法，建立能科学表征混凝土类材料包括剪切增强效应和应变率效应在内的复杂动态力学行为的高精度数值模型。在此基础上，定量分析剪切增强效应和应变率效应对混凝土类材料状态方程行为的影响，并指出剔除平板撞击实验中剪切增强和应变率耦合效应所面临的困难。结果表明：利用Kong-Fang模型和SPG算法可精确模拟混凝土类材料包括剪切增强效应和应变率效应在内的复杂动态力学行为；为实现爆炸冲击荷载作用下混凝土类材料在高-中-低压下动态力学行为的精细化模拟，要依据可靠的状态方程行为实验数据建立混凝土类材料宽广压力范围状态方程；在利用平板撞击实验数据标定状态方程参数时，须剔除剪切增强和应变率耦合效应的影响；建立混凝土类材料宽广压力范围状态方程存在悖论，利用数值迭代策略可能是解决困难的有效手段。研究结论可为后续利用数值迭代策略剔除剪切增强效应和应变率效应对混凝土类材料状态方程的影响，并进一步建立爆炸冲击荷载作用下混凝土类材料高精度宽广压力范围状态方程提供依据。Abstract: To investigate the shear-enhanced compaction effect and strain-rate effect on the equation of state (EoS) of concrete-like materials subjected to blast and impact loadings, high-fidelity numerical simulations were performed based on two types of EoS behavior tests for cement mortar, including hydrostatic compression tests and flyer-plate impact tests. These simulations employed the Kong-Fang hydro-elasto-plastic model for concrete-like materials and were implemented using the smoothed particle Galerkin (SPG) algorithm in LS-DYNA, enabling accurate reproduction of complex dynamic mechanical behaviors, including the shear-enhanced compaction effect and strain-rate effect. Based on the high-fidelity numerical simulations described above, a quantitative analysis was conducted to investigate the influence of the shear-enhanced compaction effect and strain-rate effect on EoS behavior of concrete-like materials, and the challenges associated with eliminating the shear-enhanced compaction and strain-rate coupling effects in flyer-plate impact tests were systematically identified. The results demonstrate that the Kong-Fang model, when combined with the SPG algorithm, can accurately simulate the complex dynamic mechanical behaviors of concrete-like materials, including shear-enhanced compaction effect and strain-rate effect. To achieve high-precision simulation of dynamic mechanical behaviors of concrete-like materials subjected to blast and impact loadings across high-medium-low pressure ranges, it is essential to establish an EoS with a wide-range pressure based on experimental data from EoS behavior tests. However, shear-enhanced compaction and strain-rate coupling effects should be eliminated when using flyer-plate impact test data to calibrate the EoS parameters. A paradox arises in the establishment of EoS with wide-range pressure for concrete-like materials, and the application of numerical iteration correction methodology may represent an effective approach to resolving this challenge. These findings provide a theoretical foundation for the future development of a numerical iteration correction methodology to eliminate the shear-enhanced compaction effect and strain-rate effect on the EoS of concrete-like materials, thereby facilitating the establishment of a high-precision EoS with a wide range of pressure for concrete-like materials subjected to impact and blast loadings.
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图 2 水泥砂浆HC实验加载/卸载曲线
Figure 2. Loading-unloading curves from HC experiment for cement mortar
图 3 撞击速度为288 m/s的对称FPI实验粒子速度时程曲线与数值计算预测结果的对比
Figure 3. Comparison of particle velocity-time histories recorded in symmetric FPI experiment at an impact velocity of 288 m/s with ones predicted by numerical computation
图 4 撞击速度为475 m/s的正向FPI实验粒子速度时程曲线与数值计算预测结果的对比
Figure 4. Comparison of particle velocity-time histories recorded in normal FPI Experiment at an impact velocity of 475 m/s with ones predicted by numerical computation
图 8 根据三轴压缩实验数据标定的水泥砂浆强度面参数
Figure 8. Failure surface parameters for cement mortar calibrated by triaxial compression experimental data
图 9 根据HC实验数据标定EoS参数（EoS-HC）
Figure 9. Calibrated EoS parameters based on HC data (EoS-HC)
图 10 水泥砂浆状态方程行为实验数值模拟几何模型及边界条件
Figure 10. Geometry and boundary conditions of numerical models for EoS behavior tests of cement mortar
图 11 水泥砂浆状态方程行为实验数值模型网格敏感性分析
Figure 11. Mesh-size sensitivity of numerical models for EoS behavior experiments of cement mortar
图 12 HC实验数值模拟结果与相应实验结果的对比
Figure 12. Comparison of numerical predictions for the HC experiment with the corresponding experimental data
图 13 不同速度下FPI实验数值模拟预测的σx-μ关系与实验结果的对比
Figure 13. Comparison of the σx-μ relation between the FPI experiment data and numerical predictions at different impact velocities
图 14 数值模拟预测的撞击速度为288 m/s的对称FPI实验水泥砂浆靶体压力时程曲线
Figure 14. Numerically predicted pressure-time histories in cement mortar target for symmetric FPI experiment at an impact velocity of 288 m/s
图 15 数值模拟预测的撞击速度为288 m/s的对称FPI实验水泥砂浆靶体损伤云图
Figure 15. Numerically predicted damage in cement mortar target for symmetric FPI experiment at a velocity of 288 m/s
图 16 根据FPI实验数据标定EoS参数（EoS-FPI）
Figure 16. Calibrated EoS parameters based on FPI test data (EoS-FPI)
图 17 基于EoS-FPI的水泥砂浆2类状态方程行为实验数值模拟与实测结果对比
Figure 17. Comparison of experimental data with numerical predictions using EoS-FPI
图 18 基于2种EoS参数进行数值模拟得到的HC和FPI实验预测结果的对比
Figure 18. Comparison of numerical predictions based on two sets of EoS parameters
图 19 剪切增强效应和应变率效应的对比
Figure 19. Comparison between shear-enhanced compaction effect and strain-rate effect
表 1 水泥砂浆配合比和力学性能参数
Table 1. Mix ratios and mechanical property parameters of cement mortar
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表 2 不同撞击速度下水泥砂浆FPI实验结果[2]
Table 2. FPI experimental data for cement mortar at different impact velocities[2]
对称FPI实验 正向FPI实验 撞击速度/(m·s−1) 粒子速度/(m·s−1) 纵波波速/(m·s−1) 撞击速度/(m·s−1) 粒子速度/(m·s−1) 纵波波速/(m·s−1) 45 22.5 3055 314 274.9 2041 61 31.5 2160 475 411.7 2370 82 41.0 1996 601 508.4 2827 100 50.0 2140 777 656.9 2908 114 57.0 1613 957 787.8 3546 146 73.0 1336 1560 1230.8 4635 170 85.0 1282 1970 1526.1 5373 212 106.0 1330 214 107.0 1242 288 144.0 1454
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表 3 水泥砂浆Kong-Fang模型的状态方程参数
Table 3. Equation-of-state parameters of the Kong-Fang model for cement mortar
项目 μ1 μ2 μ3 μ4 μ5 μ6 μ7 μ8 μ9 μ10 EoS-HC 0 0.0038 0.0221 0.0448 0.0656 0.0875 0.1119 0.1314 0.1538 0.1788 EoS-FPI 0 0.0052 0.0201 0.0512 0.0856 0.1312 0.1701 0.2014 0.2437 0.2817 项目 p1/GPa p2/GPa p3/GPa p4/GPa p5/GPa p6/GPa p7/GPa p8/GPa p9/GPa p10/GPa EoS-HC 0 0.0148 0.0793 0.1440 0.2037 0.2728 0.3663 0.4533 0.5718 0.7271 EoS-FPI 0 0.1662 0.3276 0.4521 0.5863 0.9061 1.3952 1.9939 3.3863 5.5687
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