Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single-Crystal Plasticity

This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced-strain elements; and we illustrate the approach in an important area of application, namely, single-crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general

Bi-stability resistant to fluctuations

We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing effect of random perturbations. As an inspiration we use the power stroke machinery of skeletal muscles, which ensures at sub-micron scales and finite temperatures a swift recovery of an abruptly applied slack. In addition to hypersensitive response at finite temperatures, our prototypical Brownian snap spring also exhibits criticality at special values of parameters which is another potentially interesting property for micro-scale engineering applications

Simplified Energy Landscape for Modularity Using Total Variation

Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in these applications, and identifying them gives insight into the overall organization of the network. One common quality function used to identify community structure is modularity. In Hu et al. [SIAM J. App. Math., 73(6), 2013], it was shown that modularity optimization is equivalent to minimizing a particular nonconvex total variation (TV) based functional over a discrete domain. They solve this problem, assuming the number of communities is known, using a Merriman, Bence, Osher (MBO) scheme. We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain, again, assuming the number of communities is known. Furthermore, we show that modularity has no convex relaxation satisfying certain natural conditions. We therefore, find a manageable non-convex approximation using a Ginzburg Landau functional, which provably converges to the correct energy in the limit of a certain parameter. We then derive an MBO algorithm with fewer hand-tuned parameters than in Hu et al. and which is 7 times faster at solving the associated diffusion equation due to the fact that the underlying discretization is unconditionally stable. Our numerical tests include a hyperspectral video whose associated graph has 2.9x10^7 edges, which is roughly 37 times larger than was handled in the paper of Hu et al.Comment: 25 pages, 3 figures, 3 tables, submitted to SIAM J. App. Mat

Doctor of Philosophy

dissertationThe outstanding surge in hydrocarbon production from unconventional reservoirs is unprecedented. Profitable oil prices and new technologies have untapped massive oil and gas resources in recent years. However, the correct exploitation of these resources has been dampened by the lack of understanding of these systems. Research efforts to understand and properly assess unconventional resources have exploded in the literature. In this research work, a series of advancements in reservoir production analysis, simulation modeling, and simulation development are made. A semi-analytical method based on conventional material balance was developed to approximate reservoir pressure distributions and permeability. One of the strengths of this method is that it only requires limited information to be viable. Reservoirs with dry gas and/or high gas oil ratios are handled with an additional average pressure correction factor that takes gas compressibility into account. Hence, this method can be used for any type of fluid and fluid flow as long as the correct material balance formulation and surrogate curves are employed. Verification of the method is made through comparison with synthetic data and a field case study. Furthermore, a standardized simplification workflow for hydraulically stimulated reservoirs was introduced. The aim of this workflow is to guide the engineer when developing a simplified reservoir simulation model with multiple wells and fractures. Simplified models have been around for a long time in the literature, however, their applicability to field-scale projects is very limited. Models that result from the application of this workflow are shown to retain the low simulation run-times characteristic of popular single-fracture models. In addition, fluid rate results from the proposed workflow models are in good agreement with results from full-scale simulation models. This is not the case for the single-fracture model which loses accuracy as the complexity of the project grows. Lastly, a new discrete fracture model formulation is implemented in a control-volume finite element simulator. This new fracture model provides fractures with their own control volumes and gives them freedom to be placed anywhere in the matrix domain. Verification of this implementation is made through comparison with analytical expressions and other well-established simulators

Naturally fractured tight gas reservoir detection optimization. Annual report, September 1993--September 1994

This report is an annual summarization of an ongoing research in the field of modeling and detecting naturally fractured gas reservoirs. The current research is in the Piceance basin of Western Colorado. The aim is to use existing information to determine the most optimal zone or area of fracturing using a unique reaction-transport-mechanical (RTM) numerical basin model. The RTM model will then subsequently help map subsurface lateral and vertical fracture geometries. The base collection techniques include in-situ fracture data, remote sensing, aeromagnetics, 2-D seismic, and regional geologic interpretations. Once identified, high resolution airborne and spaceborne imagery will be used to verify the RTM model by comparing surficial fractures. If this imagery agrees with the model data, then a further investigation using a three-dimensional seismic survey component will be added. This report presents an overview of the Piceance Creek basin and then reviews work in the Parachute and Rulison fields and the results of the RTM models in these fields

Phase-field Modeling of Phase Changes and Mechanical Stresses in Electrode Particles of Secondary Batteries

Most storage materials exhibit phase changes, which cause stresses and, thus, lead to damage of the electrode particles. In this work, a phase-field model for the cathode material NaxFePO4 of Na-ion batteries is studied to understand phase changes and stress evolution. Furthermore, we study the particle size and SOC dependent miscibility gap of the nanoscale insertion materials. Finally, we introduce the nonlocal species concentration theory, and show how the nonlocality influences the results