A model for the mechanical response of electrode particles induced by lithium diffusion in Li-ion batteries

A constitutive model is derived for the viscoplastic response of a host medium driven by diffusion of guest atoms. With reference to the trapping concept, two states of a guest atom are distinguished: mobile and immobilized (due to alloying with the host matrix). Reaction–diffusion equations for the transport of mobile atoms and their trapping, as well as stress–strain relations for the mechanical behavior of the host material, are developed based on the free-energy imbalance inequality. The constitutive equations are applied to the analysis of stresses in a spherical electrode particle under insertion of lithium. Numerical simulation demonstrates the ability of the model to predict (i) formation of a sharp interphase between regions rich and poor in guest atoms, (ii) propagation of the interphase with a constant velocity, and (iii) size-dependent fracture of electrode particles.