Battery packs in electric vehicles consist of several battery modules, each containing several battery cells with numerous layers (electrodes, separators and current collector layers. A finite element model that can capture the stresses on the layer level would be extremely large in order to resolve the details. In the present paper, a novel homogenization method is presented which is based on three-dimensional laminate theory. The number of finite elements for the simulation of stresses in batteries can in this way be drastically reduced. Based on a homogenized solution, layer-level stresses can then be determined in a post-processing step. The present formulation is adaptive and fast, eliminating the need to model individual layers. It allows for non-linear elastic behavior of active layers that undergo swelling and separator layers as well as elastic-plastic behavior of current collectors. Three realistic battery structures subjected to swelling in electrode layers have been simulated: 1. free jellyroll, 2. jellyroll enclosed by a stiff enclosure, and 3. battery module consisting of 10 cells. The presented homogenized method allows for the inclusion of battery cells as parts of larger models representing vehicle structures and facilitates studying the interaction between batteries and surrounding structures.