To illustrate this problem, a 1-D continuum model was developed to simulate the discharging process of an all-solid-state Li-ion battery, which is composed of Li as the anode, LiC_OO₂ as the cathode, and Li₃PO₄ as the electrolyte. The parameters were taken from a thin-film battery model that has fitted to experimental data. We incorporated the effect of the imperfect contact into this model by assuming the current and Li concentration will be localized at the contacted area. We correlated the percentage of lost contact area with the discharging capacity and energy. We observed that the capacity and energy decrease with the loss of contact area and discharge rate. For example, when discharging at 1 C-rate, the capacity decreased 20% as the contact area losses 19.8%. At a higher discharging rate of 32 C, the capacity dropped quickly to be less than 20% when the contact area losses 1.52%. 

Since Li₃PO₄ and LiC_OO₂ are both ceramic materials and their initial contact area is non-perfect after the fabricating process. We applied the Johnson-Kendall-Roberts (JKR) model, which is appropriate for elastic deformation and adhesive contact, to estimate the applied pressure that can recover the loss of contact to the initial condition. We found that it is more effective to apply the pressure when the battery just starts to decay when the battery capacity loss is less than 10%. Therefore, in practical application, this model and method can be used to estimate the extent of the loss of contact area during the operation of the all-solid-state Li-ion battery, and further suggesting how much pressures should be applied to recover the capacity.