Semi-analytical solution of lithiation-induced stress in a finite cylindrical electrode

In this work, we study the spatiotemporal evolution of stresses in a finite cylindrical electrode during lithiation without the consideration of stress-limited lithiation. Using Boussinesq-Papkovich functions and orthogonal series, we derive semi-analytical solutions of lithium concentration and stresses in the finite cylindrical electrode under traction-free condition and potentiostatic operation. Numerical calculations are performed for a cylindrical electrode with the length-to-diameter ratio of 2, and the numerical results are compared with the results from finite element simulation via the multi-physics software (COMSOL). There is good agreement between the numerical results and the simulation results for the spatiotemporal distribution of lithium concentration, and there exists slight difference between the numerical results and the simulation results for the radial and hoop stresses with the relative maximum difference of similar to 9% for the radial stress at the dimensionless time of 0.02. The von-Mises stress on the plane of z=0 reaches maximum at surface, which decreases with the increases of the state of charge. The result suggests that local plastic deformation will start immediately at surface under the potentiostatic operation if the electrode can experience plastic deformation.