Perturbation solutions of the diffusive chemo-mechanical coupling problem without a failure of local Fick’s law.

*(English)*Zbl 1446.74126Summary: Silicon electrodes of lithium-ion batteries have a remarkable diffusive chemo-mechanical coupling effect during lithiation and delithiation. In order to study the variation of stresses and concentration distribution in the electrode, a nonlinear partial differential equation for the concentration is usually derived using the thermal analogy method and Fick’s laws, in the case without a failure of local Fick’s law. However, due to the nonlinearity of the equation and the boundary conditions, it is generally difficult to get the analytic solution. In this paper, by using the dimensionless quantities, the perturbation solutions are obtained for two fundamental problems, that is, the semi-infinite and the cylinder, which appears to be semi-analytic and easy for the numerical calculation. The results match with the numerical solutions very well, when the charge current density is controlled in a relatively appropriate range. The semi-analytic solutions show that the compressive stress promotes the diffusion of lithium in the electrode during lithiation, which cannot be neglected, compared with the condition without considering the coupling effect.

##### MSC:

74F25 | Chemical and reactive effects in solid mechanics |

74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |

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\textit{X. Shen} and \textit{Y. Wan}, Math. Mech. Solids 25, No. 3, 804--819 (2020; Zbl 1446.74126)

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