As LiCoO2 cathodes are charged, delithiation of the LiCoO2 active material leads to an increase in the lattice spacing, causing swelling of the particles. When these particles are packed into a bicontinuous, percolated network, as is the case in a battery electrode, this swelling leads to the generation of significant mechanical stress. In this study we performed coupled electrochemical-mechanical simulations of the charging of a LiCoO2 cathode in order to elucidate the mechanisms of stress generation and the effect of charge rate and microstructure on these stresses. Energy dispersive spectroscopy combined with scanning electron microscopy imaging was used to create 3D reconstructions of a LiCoO2 cathode, and the Conformal Decomposition Finite Element Method is used to automatically generate computational meshes on this reconstructed microstructure. Replacement of the ideal solution Fickian diffusion model, typically used in battery simulations, with a more general non-ideal solution model shows substantially smaller gradients of lithium within particles than is typically observed in the literature. Using this more general model, lithium gradients only appear at states of charge where the open-circuit voltage is relatively constant. While lithium gradients do affect the mechanical stress state in the particles, the maximum stresses are always found in the fully-charged state and are strongly affected by the local details of the microstructure and particle-to-particle contacts. These coupled electrochemical-mechanical simulations begin to yield insight into the partitioning of volume change between reducing pore space and macroscopically swelling the electrode. Finally, preliminary studies that include the presence of the polymeric binder suggest that it can greatly impact stress generation and that it is an important area for future research.