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.
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