One of the major catastrophic events in the accidents involving electric vehicles is the electric short circuit, leading to the thermal runaway, and possible fire and explosion. The short circuit is a result of the development of local or through-thickness fracture inside a cell. Fracture of the discrete layered structure of lithium-ion batteries is a complex problem involving six materials with completely different deformation and fracture properties. The homogenized model of the deformation of batteries has emerged as the best compromise between simplicity and accuracy, and therefore the well-established Deshpande-Fleck model of crushable foams is used in the present analysis to describe the deformation behavior. For the fracture description of battery cells, the authors follow the experience accumulated over the decades in predicting failure of metals and geomaterials. The constitutive description of these classes of materials gained in complexity, requiring elaborated experimental techniques for the determination of material parameters. However, the choice of possible tests for pouch or cylindrical cells is very limited, which hinders the complexity in fracture models. Those tests are typically in-plane and out-of-plane compression tests because it is almost impossible to subject an individual pouch battery to tensile or shear loading. Therefore, out of vast literature in the field of fracture, only the simplest models are considered. In this study, the seven simplest fracture models, involving only one or maximum two material constants, are coupled with the homogenized Deshpande-Fleck model to study the fracture behavior of pouch cells. Their performance is critically evaluated in terms of the capability of predicting the initiation and propagation of crack under mechanical transverse loading.