Electro-mechanical Li-Ion Cell Model considering the composite Graphite-Silicon Structure of the negative Electrode

To increase the volumetric energy density modern high-energy Lithium-Ion cells consist of Graphite/Silicon ($\mathbf{G r} / \mathbf{S i}$) composite negative electrodes. Due to the high volume expansion of up to 300% caused by (de)lithiation of Si, challenges arise by the usage of $\mathbf{G r} / \mathrm{Si}$-electrodes to prevent accelerated degradation. Therefore, accurate models to predict the cell expansion and pressure are of increasing interest. To investigate the mechanical behavior, half-cell Equivalent Circuit Models (ECMs) are coupled with a solid and liquid diffusion model in this article. The current density distribution among $\mathbf{S i}$ - and Gr -particles is determined by the assumption of an ideal parallel-connected of the active materials. An electrochemical dilatometer is used to measure the electrode expansion. Based on these measurements and literature values of volume changes of the crystal structure, changes of the pore volume are estimated. For the cell expansion and force development a visco-elastic model is implemented by using a spring in serial to a Kelvin-Voigt-Model. Simulations show high agreement with experimental data and literature values regarding cell voltage and expansion.