Diffusion Induced Stresses in Cylindrical Lithium-Ion Batteries: Analytical Solutions and Design Insights

Analytical solutions of diffusion induced stress in a cylindrical multilayer electrode during lithiation are obtained. Design insights are provided by analyzing the diffusion induced stress as a function of geometrical parameters, material properties and charging procedure. It is found that the stress is induced not only by the Li-ion concentration inhomogeneity in the active layer materials, but also by the restriction of the lithiated active layer by the current collector. Curvature and thickness of electrode, as well as rigidity of current collector, have great impacts on the stresses. The maximum stress during charging can be minimized by reducing the thickness of electrode, employing soft material for the current collector and decreasing the thickness of current collector. It is also found that the ratio of maximum stress to minimum stress in the active layers can be reduced from 2.1 to 1.1 if the radius-to-thickness ratio of electrode is increased from 1 to 10. Employing this radius-to-thickness ratio provides that the maximum stresses are quite uniform in the two active layers attached on current collector, independently of lithiation or delithiation. Finally, an optimized charging procedure is suggested based on the diffusion induced stresses, i.e. galvanostatic first followed by potentiostatic.