Since Atom Probe Tomography reconstruction is based on ion back projection onto the emitter surface, understanding of the evolution dynamics of the tip shape is essential to get an accurate picture of the initial sample. In this article, an analytical approach is presented to dynamically describe the morphology evolution of complex multilayer structures during field evaporation. The model is mostly founded on the common continuity hypothesis, except for the classical hemispherical description of the tip apex, which is extended to a wider class of a constant mean curvature surface of revolution, the Delaunay surfaces. The results obtained from this approach are comparable with standard numerical simulations, but the analytical character of the model gives more insight into the principles driving the emitter morphology. In particular, a complete picture of curvature evolution during the transition from one layer to another is provided. Additionally, a field evaporation threshold for tip fracture in a bilayer sample is highlighted.