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.

The high-pressure equation of state is the basis of studying the failure mechanism of materials and the propagation law of shock waves under explosion or impact loading. The state of rock has a wide range of applications in the numerical calculation of mining, meteorite impact cratering, rock impact protection, etc. Using a two-stage light gas gun and Photon Doppler Velocimeter(PDV), the Hugoniot relationship, high-pressure equation of state and volume strain equation of red sandstone were studied. The lowest and the highest impact pressure generated by the collision were 7.2 GPa and 19.4 GPa, respectively, and the lowest and the highest planar impact velocity were 0.88 km/s and 1.97 km/s, respectively. At the same time, optic probes were used to measure the shock wave velocity of rock samples. However, The Hugoniot-Elastic-Limit(HEL) point of the red sandstone was not found in the free surface velocity profile recorded by the PDV, indicating that the red sandstone was in a near-fluid state within this impact pressure range. Furthermore, the shock wave velocity D and particle velocity u were linearly fit by the least square method, and the Hugoniot parameters of the red sandstone were C₀=3.04 and λ=1.14, respectively. In addition, the relationship between the volumetric strain η and the impact pressure P were obtained by polynomial fitting, which was P=116η-745η²+1845η³, and the nonlinear fitting coefficient was 0.993. The Hugoniot equation of state and bulk strain equation of red sandstone obtained in this work can provide reference data for numerical calculation and engineering application in red sandstone rock blasting, shock protection engineering, and so on.