Browsing by Subject "Fragmentation"

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

This dissertation explores formal fragmentation in the modernist novel. It shows that such fragmentation not only represents the historical conditions of modernism, but also posits the potential for new forms of human relation. Each chapter explores test cases of this potential through a close analysis of a novel and argues that in order to understand such literary structure one must look beyond literature to the wider episteme of modernism. Each chapter therefore positions literature alongside a related field, where the affinities are shown to be found not in a shared content but in a shared form. The chapters include explorations of: the problem of language in Faulkner’s As I Lay Dying read alongside advertising; the problem of continuity and fragmentation in Ford’s Parade’s End read alongside security and administrative governance; and the problem of perception in Woolf’s The Waves read alongside physics. As the discussion of these pairings proceeds from chapter to chapter, it is shown that the fragmentation of each respective novel reveals an increasingly successful utopian experiment in alternative forms of human relationality. At an additional register, this dissertation also shows that such experimentation requires a redefined role for the critic, for the novels each draw the reader into their texts by not only representing but enacting fragmentation in a way that requires the reader to participate in the utopian experiment. Through the practice of criticism, the critic is therefore implicated in the modernist project, and complicit in all of the political and ethical concerns the project carries.