Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

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.

Mechanical defenses in leaves eaten by Costa Rican howling monkeys (Alouatta palliata).

Primate species often eat foods of different physical properties. This may have implications for tooth structure and wear in those species. The purpose of this study was to examine the mechanical defenses of leaves eaten by Alouatta palliata from different social groups at Hacienda La Pacifica in Costa Rica. Leaves were sampled from the home-ranges of groups living in different microhabitats. Specimens were collected during the wet and dry seasons from the same tree, same plant part, and same degree of development as those eaten by the monkeys. The toughness of over 300 leaves was estimated using a scissors test on a Darvell mechanical tester. Toughness values were compared between social groups, seasons, and locations on the leaves using ANOVA. Representative samples of leaves were also sun-dried for subsequent scanning electron microscopy and energy dispersive x-ray (EDX) analyses in an attempt to locate silica on the leaves. Both forms of mechanical defense (toughness and silica) were found to be at work in the plants at La Pacifica. Fracture toughness varied significantly by location within single leaves, indicating that measures of fracture toughness must be standardized by location on food items. Monkeys made some food choices based on fracture toughness by avoiding the toughest parts of leaves and consuming the least tough portions. Intergroup and seasonal differences in the toughness of foods suggest that subtle differences in resource availability can have a significant impact on diet and feeding in Alouatta palliata. Intergroup differences in the incidence of silica on leaves raise the possibility of matching differences in the rates and patterns of tooth wear.

Fractures in myelomeningocele.

BACKGROUND: In patients with myelomeningocele (MMC), a high number of fractures occur in the paralyzed extremities, affecting mobility and independence. The aims of this retrospective cross-sectional study are to determine the frequency of fractures in our patient cohort and to identify trends and risk factors relevant for such fractures. MATERIALS AND METHODS: Between March 1988 and June 2005, 862 patients with MMC were treated at our hospital. The medical records, surgery reports, and X-rays from these patients were evaluated. RESULTS: During the study period, 11% of the patients (n = 92) suffered one or more fractures. Risk analysis showed that patients with MMC and thoracic-level paralysis had a sixfold higher risk of fracture compared with those with sacral-level paralysis. Femoral-neck z-scores measured by dual-energy X-ray absorptiometry (DEXA) differed significantly according to the level of neurological impairment, with lower z-scores in children with a higher level of lesion. Furthermore, the rate of epiphyseal separation increased noticeably after cast immobilization. Mainly patients who could walk relatively well were affected. CONCLUSIONS: Patients with thoracic-level paralysis represent a group with high fracture risk. According to these results, fracture and epiphyseal injury in patients with MMC should be treated by plaster immobilization. The duration of immobilization should be kept to a minimum (<4 weeks) because of increased risk of secondary fractures. Alternatively, patients with refractures can be treated by surgery, when nonoperative treatment has failed.