Mechanical Stresses in Pouch Cells: a Reduced Order Model

In a pouch cell battery, the intercalation of lithium ions into the active particles means the electrodes want to expand. However, since the electrodes are attached to stiff current collectors, this expansion is constrained, leading to a macro-scale deformation and a residually stressed state. This stress state affects the electrochemistry and can also lead to mechanical degradation, causing a reduction in performance. We model the mechanical state of stress in the battery assuming a known compositional expansion of the electrodes, and use asymptotic techniques to generate reduced order models by exploiting the thin aspect ratio, as well as the large stiffness of the current collectors. We obtain analytic expressions for the stress in the bulk of the electrodes and at the interface between electrodes and current collectors, and a reduced-order equation whose solution describes the tension in the current collectors. We compare our results with full 3D finite element simulations with excellent agreement, and use our results with the battery simulation package PyBaMM to predict a realistic stress state in a discharging battery.