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A cylindrical electrode is approximated as a long cylinder in most existing models in which generalized plane strain condition/plane strain is used. Based on the theory of elasticity, analytical expressions are derived for concentration distribution and stress component in a finite-length cylindrical electrode under galvanostatic operation. Applying the superposition theorem, the Li-concentration is a sum of the concentration due to axial diffusion and the concentration due to lateral diffusion, and separation of variable method are used to solve diffusion equations separately. Employing Boussinesq-Papkovich function, the stress component distributions which are generalized for a linear combination products of the Fourier-Bessel series of exponential type are derived. The spatiotemporal of distribution of concentration and diffusion-induced stresses are calculated in a cylindrical electrode with traction-free condition. The results are compared with a simulation results calculated with a finite element software. For the concentration distribution, the numerical result and simulation result are almost identical. For the stress component, no significant difference exists between the two results, the largest relative difference for radial stress of ~4% is found at center and SOC=17.9%. The radial stress decreases with an increasing radial position, decrease to zero at the surface which is consistent with the boundary condition. The hoop stress is tensile around the center of electrode, turn to compressive near surface. Since the tensile hoop stress is responsible for crack initiation, this suggests cracks is first to found at the center when plastic deformation is negligible. The stress component with different length to radius ratios is calculated. It is found that the stress due to lateral diffusion increases with an increase of length to radius ratios, while the stress due to axial diffusion decreases. This is because that the lateral diffusion has a greater influences on Li-concentration distribution in a cylinder electrode with increasing length to radius ratio.
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Keywords:
- Lithium-ion batteries /
- Finite-length cylindrical electrode /
- Diffusion-induced stress /
- Boussinesq-Papkovich function
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