Comparison of shock compaction models for granular materials: P -α model and mesoscale simulation

Abstract

This study examines particle velocity measurements in granular sugar to evaluate the predictive accuracy of two computational models for weak shock under flyer-plate impact: the continuum-based P-alpha Menko model and mesoscale simulations with explicit particle and pore representations. Using flyer-plate impact experiments as a benchmark, we show that both two-dimensional (2D) models can reproduce the measured particle velocity histories, but through fundamentally different mechanisms. In the P-alpha framework, applying a pressure-dependent yield strength is essential to capture the particle velocity evolution, though calibration of other constitutive parameters, such as crush-out pressure, still strongly influences the response. In contrast, mesoscale simulations are less sensitive to parameter tuning and rely critically on the physical state variable of porosity, represented in 2D as an equivalent measure of the 3D specimen. Together, these results establish that their mechanical interpretations differ: continuum parameters act as effective surrogates for grain-scale physics, whereas mesoscale modeling reveals porosity as the dominant control of macroscopic wave onset.

Figures (5)

• Figure 1: (a) Setup for computational modeling (b) Experimental data from Sheffield et al. (1998) Sheffield1998
• Figure 2: (a) Testing granular materials prepared by dry pluviation. Zone pressure results from $P$-$\alpha$ model and mesoscale simulations, respectively. The onset of the plateau in input particle velocity occurs at (b) 2.72 $\mu$sec and (c) 2.4 $\mu$sec, while the transmitted velocity reaches its plateau at (d) 7.12 $\mu$sec and (e) 6.83 $\mu$sec
• Figure 3: $P$-$\alpha$ model with porosity of 0.24, 0.27, 0.30, and 0.35
• Figure 4: (a) Comparison of shock velocities between $P$-$\alpha$ model and experimental data (b) pressure-dependent yield strength. Sensitivity analysis of $P$-$\alpha$ Menko model with respect to (c) shear modulus, (d) full crush-out pressure, $P_c$, (e) yield strength, and (f) slope of the $Y(P)$
• Figure 5: (a) The best fitting of mesoscale model with elasto-perfectly plastic model to experimental data, and (b) mesoscale model with porosity of 0.24, 0.27, 0.30, and 0.35. Sensitivity analysis of mesoscale model (c) shear modulus, and (d) yield strength. Mesoscale model with elasto-plastic behavior and linear hardening for material response: (e) Fit 1, and (f) Fit 2