Effect of combining local velocity and chemical reaction on the interaction between diffusion and stresses in large deformed electrodes

A general framework to study the effects of chemical reaction, local deformation velocity and their interaction on the two-way coupling between stress and Li diffusion in a spherical silicon electrode under galvanostatic operation is presented in this work. The reversible chemical theory is adopted as a start up to obtain the reaction equation and the influence of local deformation velocity on the flux is taken into consideration. This is such a complex problem that an analytical solution can hardly be found. Therefore, a numerical method is subsequently used to solve the derived coupled partial differential equations (PDEs) in nonlinear elasticity with finite deformation to analyze the diffusion-induced stress (DIS) in the electrode. The numerical results of lithium concentration, radial stress and hoop stress suggest that in comparison with the local deformation velocity, the reversible chemical reaction plays a much more significant role in altering the distribution of DIS and Li concentration. The local deformation could raise the concentration gradient and result in larger magnitude of DIS, while the chemical reaction could hinder the diffusion process as well as the swelling of the electrode material. It is also observed that the local deformation could promote the chemical reaction near the surface of the electrode but retard it in the core. Furthermore, the effects of the current density are also discussed. For a smaller lithiation rate, the interaction between chemical reaction and local deformation has a tendency of decreasing, which could have significant contribution to enhance the stability level and the cycle performance of lithium-ion batteries.