Numerical calculation of lithiation-induced stress in a spherical electrode: Effect of lithiation-induced structural damage

The improvement of the long-time stability of metal-ion batteries requires the understanding of structural integrity of electrode materials during electrochemical cycling. Using the correlation between damage state variable, local concentration and concentration gradient of solute atoms proposed by Yang [Journal of Energy Storage 45 (2022) 103748], we analyze the effects of lithiation-induced structural damage/degradation on the stress evolution in a spherical electrode in the framework of linear elasticity with the coupling between diffusion and stress under respective potentiostatic and galvanostatic operation. Without the contribution of the concentration gradient to structural damage/degradation, the effective stress exhibits an increasing trend, reaches local maximum and then decreases with the increase of the lithiation time at a spatial position away from the center of the spherical electrode for both the potentiostatic and galvanostatic operations. The largest maximum effective stress is present at the surface of the spherical electrode immediately after the onset of the lithiation for potentiostatic operation and inside the spherical electrode for galvanostatic operation. The concentration gradient causes less structural damage/degradation under galvanostatic operation than under photentiostatic operation due to that galvanostatic operation introduces less concentration gradient than potentiostatic operation.