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.

The Barriers to the Integration of the Uterine Balloon Tamponade into South Africa and Ghana's Health Systems for the Management of Postpartum Hemorrhage

Background

Postpartum hemorrhage is the most significant contributor to maternal mortality globally, claiming 140,000 lives annually. Postpartum hemorrhage is a leading cause of maternal death in South Africa, with the literature indicating that 80 percent of the postpartum hemorrhage deaths in South Africa are avoidable. Ghana, as of 2010, witnesses 2700 maternal deaths annually, primarily because of poor quality of care in health facilities and services being difficult to access. As per WHO recommendations, uterotonics are integral to treating postpartum hemorrhage as soon as it is diagnosed. In case of persistent bleeding or limited availability of uterotonics, the uterine balloon tamponade (UBT) can be used as a second line of defense. If both these measures are unable to counter the bleeding, providers must perform surgical interventions. Literature on the UBT, as one tool in the protocol to address postpartum hemorrhage, has shown it to have success rates ranging from 60 to 100 percent. Despite the potential to lower the number of postpartum hemorrhage deaths in South Africa and Ghana, the UBT has not been incorporated widely in South Africa and Ghana. The aim of this study is to describe the barriers involved with integrating the UBT into South Africa and Ghana’s health systems to address postpartum hemorrhage.

Methods

The study took place in multiple sites in South Africa (Cape Town, Johannesburg, Durban and Mpumalanga) and in Accra, Ghana. South Africa and Ghana were selected because postpartum hemorrhage contributes greatly to their maternal mortality numbers and there is potential in both countries to lower those rates through greater use of the UBT. A total of 25 participants were interviewed through purposive sampling, snowball sampling and participant referrals, and included various categories of stakeholders integral to the integration process of a medical device. Individual in-depth interviews were used for data collection, with interview questions being tailored to each stakeholder category. The focus of the interviews was on the protocol used to counter postpartum hemorrhage, the frequency with which the UBT is used as part of the protocol, and the process of integrating it into the South Africa and Ghana’s health systems. The data collected were coded using NVivo and analyzed using content analysis.

Results

The barriers to integration of the uterine balloon tamponade to address postpartum hemorrhage in South Africa and Ghana were evident on the political, economic and health delivery levels. The results indicated that the barriers to integration in South Africa included the low recognition of postpartum hemorrhage as a problem, the lack of clarity surrounding the role of the Medicines Control Council as a regulatory body for medical devices, and low awareness of the UBT as an intervention to control postpartum hemorrhage. The barriers in Ghana were the cash constraints experienced by the Ghana Health Services to fund medical devices, a heavy reliance on donors for funding, and the lack of consistent knowledge on processes involving clinical trials for new medical devices in Ghana.

Conclusion

Existing literature on methods to counter postpartum hemorrhage to reduce maternal mortality has focused on and emphasized the efficacy of the UBT. Despite overwhelming evidence supporting the use of the UBT, many health systems across the world, particularly low-income countries, do not have access to the device owing to numerous barriers in integrating the device into obstetric care. This study illustrates the need to focus on incorporating the UBT into health systems for greater availability to health workers and its use as standard of care. Ultimately, this study can be used as a stepping-stone for more research on this subject, providing evidence to influence policymakers to integrate the UBT into their protocols for postpartum hemorrhage response.

Numerical detection of the Gardner transition in a mean-field glass former.

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.