PhD Final Defense – Travis A. Shoemaker

Advancing the Scalability of Polyhedral Discrete Element Modeling Through Proximity Contact Laws and Surrogate Contact Detection

Advisor: Professor Youssef M.A. Hashash

Abstract

The discrete element method (DEM) is a powerful computational framework for modeling granular materials by explicitly capturing interparticle interactions that govern macroscopic behavior. While early DEM formulations relied on spherical particles, polyhedral particle DEM enables improved representation of particle shape and higher fidelity simulation of complex geomaterials. However, two fundamental challenges limit its broader applicability: the difficulty of representing systems with extreme particle size disparities and the high computational cost of large-scale simulations.

This dissertation addresses these challenges through two advancements implemented within a unified modeling platform. A benchmarking study of open-source, research, and commercial DEM platforms informs platform selection. Among these, the IBLOKS code was selected for its computational efficiency, extensibility, and support for both conventional DEM and impulse-based DEM (iDEM) within a unified framework.

The first advancement is a novel proximity contact law that enables tractable DEM simulation of systems with extreme particle–size disparities (e.g., trillions of nanoparticles per sand particle). Drawing on concepts from statistical mechanics, the formulation implicitly represents the collective influence of nanoparticles through effective intergranular forces. The model introduces finite-range, pre-contact attractions using a compact two-parameter formulation calibrated against laboratory triaxial data at a single confining stress. Despite its simplicity, the model reproduces, without further calibration, key experimental trends across a range of confining stresses.

The second advancement is a machine-learning-based surrogate model that replaces conventional polyhedral contact detection in DEM and iDEM. Developed to overcome the contact detection bottleneck, the surrogate is trained offline using a universal dataset of particle-pair interactions, enabling scenario-independent generalization across problem types without retraining. This versatility is demonstrated by applying the same surrogate to both rockfall and granular column collapse simulations, and the surrogate is also used interchangeably between DEM and iDEM formulations. Furthermore, the surrogate maintains numerical stability using half-precision arithmetic, reducing memory usage by up to 85%. The surrogate achieves up to a sevenfold contact detection speedup and enables simulations exceeding 200 million polyhedral particles on a single computing node, reaching previously unattainable simulation scales.

By addressing limitations in both multiscale interaction representation and computational performance, this work advances polyhedral DEM toward a more scalable and practical tool, enabling simulations of granular materials at unprecedented scales.