Parallel Level-Set DEM (LS-DEM) Development and Application to the Study of Deformation and Flow of Granular Media

Abstract

We present a systematic investigation of computational approaches to the modeling of granular materials. Granular materials are ubiquitous in everyday life and in a variety of engineering and industrial applications. Despite the apparent simplicity of the laws governing particle-scale interactions, predicting the continuum mechanical response of granular materials still poses extraordinary challenges. This is largely due to the complex history dependence resulting from continuous rearrangement of the microstructure of granular material, as well as the mechanical interlocking due to grain morphology and surface roughness. X-Ray Computed Tomography (XRCT) is used to characterize the grain morphology and the fabric of the granular media, naturally deposited sand in this study. The Level-Set based Discrete Element Method (LS-DEM) is then used to bridge the granular behavior gap between the micro and macro scale. The LS-DEM establishes a one-to-one correspondence between granular objects and numerical avatars and captures the details of grain morphology and surface roughness. However, the high-fidelity representation significantly increases the demands on computational resources. To this end a parallel version of LS-DEM is introduced to significantly decrease the computational demands. The code employs a binning algorithm, which reduces the search complexity of contact detection from O(n2) to O(n), and a domain decomposition strategy is used to elicit parallel computing in a memory- and communication-efficient manner. The parallel implementation shows good scalability and efficiency. High fidelity LS avatars obtained from XRCT images of naturally deposited sand are then used to replicate the results of triaxial tests using the new, parallel LS-DEM code. The result show that both micro- and macro-mechanical behavior of natural material is well captured and is consistent with experimental data, confirming experimental observation that the primary source of peak strength of sand is the mechanical interlocking between irregularly shaped grains. Specifically, triaxial test simulations with a flexible membrane produce a very good match to experimentally observed relationships between deviatoric stress and mobilized friction angle for naturally deposited sand. We then explore the viability of modeling dynamic problems with a new formulation of an impulse based LS-DEM. The new formulation is stable, fast, and energy conservative. However, it can be numerically stiff when the assembly has substantial mass differences between particles. We also demonstrate the feasibility of modeling deformable structures in the rigid body framework and propose several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contacts and dynamic collisions. Finally, we extend the impulse-based LS-DEM to include arbitrarily shaped topographic surfaces and exploit its algorithmic advantages to demonstrate the feasibility of modeling realistic behavior of granular flows. The novel formulation significantly improves performance of dynamic simulations by allowing larger time steps, which is advantageous for observing the full development of physical phenomena such as rock avalanches, which we present as an illustrative example.