Multi-Scale Simulation and Optimization of Lithium Battery Performance

The performance and degradation of lithium batteries strongly depends on electrochemical, mechanical, and thermal phenomena. While a large volume of work has focused on thermal management, mechanical phenomena relevant to battery design are not fully understood. Mechanical degradation of electrode particles has been experimentally linked to capacity fade and failure of batteries; an understanding of the interplay between mechanics and electrochemistry in the battery is necessary in order to improve the overall performance of the battery. A multi-scale model to simulate the coupled electrochemical and mechanical behavior of Li batteries has been developed, which models the porous electrode and separator regions of the battery. The porous electrode includes a liquid electrolyte and solid active materials. A multi-scale finite element approach is used to analyze the electrochemical and mechanical performance. The multi-scale model includes a macro- and micro-scale with analytical volume-averaging methods to relate the scales. The macro-scale model describes Li-ion transport through the electrolyte, electric potentials, and displacements throughout the battery. The micro-scale considers the surface kinetics and electrochemical and mechanical response of a single particle of active material evaluated locally within the cathode region. Both scales are non-linear and dependent on the other. The electrochemical and mechanical response of the battery are highly dependent on the porosity in the electrode, the active material particle size, and discharge rate. Balancing these parameters can improve the overall performance of the battery. A formal design optimization approach with multi-scale adjoint sensitivity analysis is developed to find optimal designs to improve the performance of the battery model. Optimal electrode designs are presented which maximize the capacity of the battery while mitigating stress levels during discharge over a range of discharge rates.