The present work deals with the development of a simulation method for crack propagation in vehicle crash simulations, which is aimed to be integrated in the explicit finite element method (FEM). Especially for ultra-high strength lightweight materials, the high stress and strain concentrations occurring at the crack tip cannot be predicted with currently used element sizes. Since mesh refinement would lead to a large increase in computational time, this work investigates analytic solutions to increase the local resolution of the stress and strain fields. These solutions facilitate the use of a fracture mechanics crack propagation criterion at the crack tip. In the present work, three different variants for combining the analytical solutions with the FEM are investigated and applied for the linear-elastic crack model, and the cohesive zone model according to Dugdale. These variants are the hybrid Trefftz method (HTM), the extended finite element method (XFEM) and a submodel approach, which is referred to as the analytical submodel method (ASM) in this work. Based on an implicit implementation in MATLAB, the advantages and disadvantages of the three variants are analysed using a simple stationary mode I crack problem. Compared to the element elimination method based on continuum mechanical failure and damage models, which is currently state of the art in industrial applications, all three methods offer an improvement of the prediction quality while showing a very low mesh dependency at the same time. Since the ASM involves the least increase in computing time and is also the easiest to be integrated into an explicit crash code, this method is being further developed for the simulation of propagating cracks. In addition to the simulation methodology, the associated material characterisation is also an essential component of the overall concept. Due to this, a method for the experimental determination of the crack resistance is developed in this work. For stably growing cracks in thin-walled sheet materials, the crack tip opening angle is a suitable parameter to describe crack resistance. The tests to determine this parameter are carried out for the hot forming steel 22MnB5, as this material shows a very critical behaviour with regard to crack formation and propagation. The experimental test results are transferred to the simulation method and used to calibrate the crack tip modelling. Finally, the entire method is validated using the investigated single edge notched tensile specimens and a three-point bending test on a vehicle component. All simulations are carried out with a software prototype based on a coupling of MATLAB with LS-Dyna.