Constitutive Modelling of Granular Materials Using Cundall-Strack and Hertz-Mindlin Contact Models

Abstract This research provides empirical macroscopic constitutive models for granular materials using Cundall-Strack and Hertz-Mindlin contact models mimicking microscopic particle behaviour using YADE DEM simulations. Distinct empirical laws are proposed for each contact model, with their validity confirmed against experimental data, offering enhanced predictive capabilities for granular behavior. Triaxial simulations were conducted to highlight the impact of the selected contact model on predicting the behavior of granular materials, such as dry sand. By combining DEM simulations with empirical constitutive modeling, the study advances the understanding of granular materials in applications related to wave propagation, shock absorption, and geotechnical engineering. Mechanical properties E, G, and v were evaluated for both contact models, analyzing their dependence on confining pressure and void ratio. The results reveal that confining pressure, void ratio, and coordination number alone are insufficient to determine whether dry sand is in a loose or dense state — the contact model also plays a crucial role. Optimization techniques were used to fit multiple empirical models for E and G as functions of confining pressure and void ratio. The linear contact model predicted higher stiffness and Poisson ratio compared to the Hertz model.