All ETDs from UAB

Advisory Committee Chair

David L Littlefield

Advisory Committee Members

Stephen A Akers

Bradley Martin

Kent Danielson

Dean L Sicking

Nasim Uddin

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) School of Engineering


A complete meso-to-macro computational homogenization approach for particu-late materials has been devised and implemented in this study. Starting with experimental distributions of the micromechanical characteristics of constitutive grains, this framework uses computational modeling of mesoscale statistical ensembles to characterize effective mechanical behavior at incrementally larger mesoscopic scales. This approach is found to be useful in several ways: 1) the effective Representative Volume Element (RVE) size of particulate media can be identified using the most rigorous homogenization criterion, the Hill-Mandel macrohomogeneity condition, 2) a statistical description is possible of the effective mechanical properties of particulate media at scales below the RVE, where these properties are spurious and non-deterministic, 3) ensemble modeling results can be used to optimize and calibrate continuum models of particulate materials with Finite El-ement Analysis, 4) ensemble averages of finite strain simulations can be used to study internal state variable evolution, and 5) uncertainty quantification (UQ) of the mechanical response of particulate media is possible using propagation of uncertainty from the mesoscale ensemble results. This approach hinges on a newly developed real-time interface tracking algorithm for particle-based simulation methods that can be used to study the bounds of discrete particle aggregates such as sand. The interface tracking algorithm uses an advanced sur-face extraction technique based on the alpha shape paradigm of computational geometry. When used concurrently with particle-based methods, this algorithm can track the evolu-tion of the simulation boundaries and applying accurate micro-boundary conditions on them. The micro-boundary conditions may be of Dirichlet type, Neumann type, or mixed-orthogonal type and may be tensorial. This framework enables the heretofore limited use of particle-based simulations in upscaling studies by providing a path for homogenization and uncertainty quantification (UQ) of granular media. Thus, this framework provides an additional path for constitutive characterization of particle aggregates, particularly in hydrocode modeling of high con-finement, finite deformation phenomena.

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