Stress-induced diffusion in viscoelastic electrode particles of Li-ion batteries: a comparative analysis using chemo-viscoelastic finite element models

The role of stress-induced diffusion (SID) in influencing the mechanical response and diffusion of Li in viscoelastic electrode particles of Lithium-ion batteries is studied. A two-way coupled chemo-viscoelastic model is developed for this purpose, and the governing equations are solved via the finite element method using deal. ii, an open source C++ library. Comparative studies between one-way and two-way coupled chemo-viscoelastic models reveal that concentration and stress are initially larger for the two-way coupled model, but later they reduce in magnitude compared to the one-way coupled model. The level of filling at which the switch is observed decreases with increase in particle size. The switch occurs due to change in the sign of gradient of hydrostatic stress for a viscoelastic material from negative to positive and its concurrent effect on diffusive flux as a result of two-way coupling between stress and diffusion. Further, from comparative studies between two-way coupled elastic and viscoelastic models, it is observed that speed of filling is greater for an elastic particle in comparison to a viscoelastic particle, and the gap increases when the particle size is smaller. In addition, lower values of stresses are observed for viscoelastic electrode particles, and the difference between maximum stress generated increases with increase in particle size. Thus, the time scales associated with viscoelastic constitutive response and diffusion process alters the SID effects and could be tuned while designing electrodes to mitigate slowing down of diffusion and fracture.