[Paper Review] MC-DEM: a novel simulation scheme for modeling dense granular media

Nicolas Brodu, J.A. Dijksman+1 more|arXiv (Cornell University)|Oct 23, 2014

Granular flow and fluidized beds16 references19 citations

TL;DR

This paper introduces MC-DEM, a novel discrete element method that explicitly models interactions between multiple contacts on the same grain by incorporating linear elasticity-based deformations to improve force prediction in dense granular packings. The method achieves excellent agreement with 3D experimental data on force distributions and scaling laws, significantly outperforming traditional DEM that treats contacts as independent, without requiring finite element methods.

ABSTRACT

This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable method retains all the advantages of discrete element method (DEM) simulations and does not require the use of costly finite element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels up to the experimental maximum limit of 13\%. Comparisons with traditional non-deformable spheres approach are provided, as well as with alternative models for interactions between multiple contacts. The success of our model compared to these alternatives demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.

Motivation & Objective

• To address the poor quantitative agreement between traditional DEM simulations and experimental data in dense granular packings.
• To model the mutual influence of multiple contacts on a single grain, which is neglected in standard DEM.
• To develop a computationally efficient method that retains DEM’s simplicity while improving accuracy for dense, near-jammed systems.
• To validate the model against full 3D experimental measurements of contact forces and macroscopic response.
• To demonstrate that grain-scale deformations and cross-contact force coupling are essential for accurate simulation of dense granular media.

Proposed method

• The method computes local particle deformations using analytic linear elasticity solutions for point forces on spheres.
• It introduces corrective terms δk→c that represent the normal displacement at contact c induced by forces at other contacts k on the same grain.
• The effective overlap at each contact is updated as δc + Σk δk→c, which is then used in Hertzian force laws F ∝ (δc + Σk δk→c)^3/2.
• The model uses an empirical prefactor γ to account for boundary condition effects on cross-contact influences, improving fit to experimental data.
• All deformations are computed at the grain level without long-range interactions or finite element method (FEM) calculations.
• The approach is generalizable to other particulate systems where shape-deformation relationships are known, such as emulsions or foams.

Experimental results

Research questions

• RQ1 Can a modified DEM model that accounts for multi-contact interactions on the same grain better reproduce experimental force distributions in dense 3D granular packings?
• RQ2 How does including cross-contact force coupling via elastic deformations affect the macroscopic and microscopic response of dense granular materials?
• RQ3 To what extent does the independent-contacts assumption in standard DEM fail to capture the true mechanical behavior of dense granular systems near jamming?
• RQ4 Can a simple, analytic correction for multi-contact effects replace costly FEM-based simulations while maintaining high accuracy?
• RQ5 How do particle deformations and force propagation influence the scaling of contact forces with packing density and strain?

Key findings

• MC-DEM achieves excellent agreement with 3D experimental data from the 3DXP study, including full 3D force distributions and macroscopic force-strain response.
• The model matches the experimental scaling law F ∝ f Z φ b with high fidelity, outperforming standard DEM, which shows significant deviation.
• MC-DEM simulations exhibit only slight curvature in the unloading phase, closer to experimental data than standard DEM, though minor hysteresis remains.
• The maximum top force F in MC-DEM matches the experimental Rtop value within a small Fmin offset, indicating strong quantitative agreement.
• The model successfully captures the formation of new contacts due to grain deformation, a key mechanism absent in standard DEM.
• The empirical prefactor γ effectively compensates for boundary condition effects, suggesting that grain-level statistics can be used to model complex constraints in future models.