UC Berkeley

This dissertation provides a systematical investigation of computational approaches to mod- eling 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 his- tory dependence resulting from continuous rearrangement of the microstructure of granular material, as well as the mechanical interlocking due to grain morphology and surface rough- ness. 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. Herein, we introduce an enhanced image processing workflow for XRCT images in order to optimize the grain and fabric resolution. A parallel version of LS-DEM is then introduced to significantly decrease the computational demands. The code employs a binning algorithm, which reduced the search complexity of contact de- tection from O(n2) to O(n), and a do- main 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. Both micro- and macro-mechanical behaviors of natural materials were well captured and validated with experimental data. The results of the numerical modeling show that the primary source of peak strength of sand is the mechanical interlocking between irregularly shaped grains. Flexible membrane simulations with a rotatable loading platen were found to accurately match experimentally observed relationships between deviatoric stress and mobilized friction angle with axial shortening for naturally deposited sand. Finally, we investigated the viability of modeling dynamic problems with newly formulated impulse-based LS-DEM. The new formulation is stable, fast and energy conservative, however, it may be numerically stiff when the assembly has a substantial mass difference or badly reconstructed particles as a result of poor image resolution. We also demonstrated the feasibility of modeling deformable structures in the rigid body framework and proposed several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contact and dynamic collision. We also extended the impulse-based LS-DEM to include arbitrarily shaped topography surfaces and exploited algorithmic advantages to investigate interactions between topography and colliding objects. The novel formulation significantly improves performance and allows for larger timesteps, which is advantageous for observing the full development of physical phenomena such as rock avalanches.