A chemo-viscoelastic model and a numerical scheme to study stress-diffusion interactions in Lithium ion battery electrode particles

A mathematical model and an associated numerical framework is developed for an isotropic viscoelastic electrode particle. The ensuing differential equations are solved using FEM with the help of an open source C++ library (deal.ii). The developed model is then used to understand the effects of time dependent material property (stress relaxation function) on the stress distribution of a viscoelastic electrode particle under potentiostatic boundary conditions. In contrast to a purely elastic particle, it is observed that the radial stresses become compressive and tangential stresses tensile towards the outer end of the particle. On varying the values of the characteristic time constant (τ), it is observed that stress relaxes faster for lower values of τ when compared to larger ones. Furthermore, the interactions between stress evolution, stress relaxation function, and diffusion is studied by varying τ and the electrode particle size. The study reveals that viscoelastic effects are apparent for a range of τ depending on the particle size. Thus, the interactions between the rate of diffusion, which varies with particle sizes, and τ affect the stress relaxation function, resulting in a complex mechanical response.