Model Reformulation for Coupled Electrochemical-Mechanical Pseudo Two-Dimensional Model

Rechargeable lithium-ion batteries have been extensively used in mobile communication and portable instruments due to their high volumetric and gravimetric energy density and low self-discharge rate, leading many scientists and engineers to work towards developing lithium-ion batteries with improved performance and longer life.
The porous electrode pseudo two-dimensional (P2D) model is popular in the literature for simulating lithium-ion battery performance.(1) This model has proven versatile enough to be expanded as understanding of the battery system is improved.(2-7) However, the computationally expensive nature of the model has led to the development of reformulated and reduced order models to improve the computational efficiency of simulation.(8-13)
The P2D model has proven to accurately simulate single charge-discharge cycles, but the base model does not consider capacity fade mechanisms which are important for life evolution of the system. One source of degradation of lithium-ion batteries is the stress caused by intercalation and deintercalation of lithium into the solid active material.(14-17) Several models have been developed to calculate intercalation induced stresses of varying levels of complexity.(15, 17-21) The stress generated within the particle affects the concentration profile and cannot be captured solely by simple Fickian diffusion. Therefore, pressure induced diffusion must be included when solving for solid phase diffusion in the pseudo radial dimension r within the particle and can affect behavior at high rates of charge. Previously, the effects of stress and pressure induced diffusion have been incorporated into the single particle (SP) model using a mixed finite difference approach to discretize the solid phase concentration.(22)
Here we expand the P2D model to study the generation of stresses within the active material of a lithium-ion cell. Unlike the SP model, the P2D model allows the variation in stress to be modeled across the thickness of the electrode and is also valid for higher rates of operation. Coupling the stress-strain models with the P2D model allows better analysis of the maximum stress that occurs in the system to determine what operating conditions lead to undesirable stress generation. Reformulation in the pseudo dimension, r, based on the work by De, et al.(22) will be combined with reformulation in the primary dimension, x, based on the work by Northrop, et al.(13) in order to reduce the computational cost considerably so that control and optimization can be performed with consideration to the stress development within the cell. Better understanding can lead to better control and operation to improve the overall life of the battery, especially in high power applications.

Acknowledgements
The authors acknowledge financial support by the National Science Foundation under grant numbers CBET-0828002, CBET-0828123, and CBET-1008692, and the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

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