  We present a mechanistic theory for predicting void evolution in the Li metal
electrode during the charge and discharge of all-solid-state battery cells. A
phase field formulation is developed to model vacancy annihilation and
nucleation, and to enable the tracking of the void-Li metal interface. This is
coupled with a viscoplastic description of Li deformation, to capture creep
effects, and a mass transfer formulation accounting for substitutional (bulk
and surface) Li diffusion and current-driven flux. Moreover, we incorporate the
interaction between the electrode and the solid electrolyte, resolving the
coupled electro-chemical-mechanical problem in both domains. This enables
predicting the electrolyte current distribution and thus the emergence of local
current 'hot spots', which act as precursors for dendrite formation and cell
death. The theoretical framework is numerically implemented, and single and
multiple void case studies are carried out to predict the evolution of voids
and current hot spots as a function of the applied pressure, material
properties and charge (magnitude and cycle history). For both plating and
stripping, insight is gained into the interplay between bulk diffusion, Li
dissolution and deposition, creep, and the nucleation and annihilation of
vacancies. The model is shown to capture the main experimental observations,
including not only key features of electrolyte current and void morphology but
also the sensitivity to the applied current, the role of pressure in increasing
the electrode-electrolyte contact area, and the dominance of creep over vacancy
diffusion.
