Hugoniot Equation of State Model for Mixtures
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摘要: 高通量计算可显著提升材料的设计效率，推动冲击荷载下材料物性的前沿研究。混合物Hugoniot状态方程计算模型作为材料动力学数值模拟和材料高通量计算的关键，一直是研究热点。分别对体积可加模型和等温平均模型预估混合物Hugoniot状态方程的准确性进行了评估：前者基于热力学平衡条件，在计算混合物状态方程时并未考虑组分冲击压缩导致的温差效应；后者则利用0 K等温线，通过Mie-Grüneisen状态方程反推混合物Hugoniot冲击绝热线，等温平均模型可消除混合物中各组分因冲击压缩导致的温差效应。利用体积可加模型和等温平均模型，分别对二元合金、三元合金、二元混合物的Hugoniot状态方程进行预估，并与实测数据进行比对。计算结果表明：等温平均模型预估的混合物Hugoniot状态方程与实测数据的偏离度一般优于10%，准确度较体积可加模型更高；同时，两种模型都存在低压区预估准确性略差的现象。Abstract: High-throughput computing has become a cornerstone of modern materials design and is driving new advances in the study of shock-compressed matter. Central to these efforts is an accurate Hugoniot equation of state (EOS) for mixtures, yet existing mixture models continue to show sizeable scatter. Here we benchmarked two widely used schemes—the volume-additive model (Mod A) and the isothermal-average model (ModⅠ)—against experimental Hugoniot data for binary alloys, ternary alloys and granular mixtures. The Mod A model assumes full thermodynamic equilibrium and neglects the temperature rise of individual constituents under shock compression. The ModⅠ model, by contrast, removes this thermal contribution by deriving the mixture Hugoniot from 0 K isotherms via the Mie-Grüneisen EOS. Systematic comparison between the predicted Hugoniot EOS of binary alloy, ternary alloy, granular mixtures and the experimental data reveals that the ModⅠ model reproduces measured Hugoniot states within about 10% error across the entire pressure range studied, outperforming the Mod A model in both accuracy and robustness. Both approaches exhibit moderately larger discrepancies at low shock pressures, where thermal effects are most pronounced.
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Key words:
- mixture /
- Hugoniot /
- equation of state /
- principle of volume additivity /
- isothermal average
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图 1 冲击波阵面前后介质物性参数的突变
Figure 1. Sudden change in the physical parameters of the medium on either side of the shock front
图 2 Mod A的混合物p-V线与各组分p-V线
Figure 2. p-V curves for mixture and its component based on Mod A
图 3 (a) Mod A和ModⅠ预估钨铜烧结合金Hugoniot状态方程与实验数据的对比，(b) Mod A和ModⅠ预估模型的偏离度
Figure 3. (a) Comparison of the EOS of tungsten-copper alloy estimated by Mod A and ModⅠ with experimental data; (b) deviation degree of Mod A and ModⅠ
图 4 (a) Mod A和ModⅠ预估黄铜Hugoniot状态方程与实验数据的对比，(b) Mod A和ModⅠ预估模型的偏离度
Figure 4. (a) Comparison of the EOS of brass estimated by Mod A and ModⅠ with experimental data; (b) deviation degree of Mod A and ModⅠ
图 5 (a) Mod A和ModⅠ预估的环氧树脂-方镁石混合物的Hugoniot状态方程与实验数据的对比，(b) Mod A和ModⅠ预估模型的偏离度
Figure 5. (a) Comparison of the EOS of epoxy-periclase mixture estimated by Mod A and ModⅠ with experimental data; (b) deviation degree of Mod A and ModⅠ
图 6 (a) Mod A和ModⅠ预估的石蜡-方镁石混合物的Hugoniot状态方程与实验数据的对比，(b) Mod A和ModⅠ预估模型的偏离度
Figure 6. (a) Comparison of the EOS of paraffin-periclase mixture estimated by Mod A and ModⅠ with experimental data; (b) deviation degree of Mod A and ModⅠ
表 1 钨铜烧结合金和黄铜组分的物性参数
Table 1. Physical parameters for tungsten-copper mixture and brass alloy
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