## 2 Description of the Methodology
### Multibody Simulations  
As the process starts, an MBS is carried out with a fully non-linear model. The employed multibody package is Simpack [32], a widely used MBS software in railway dynamics simulations. It calculates all the contact patches between wheel and rail interaction. Therefore, the developed methodology allows calculating rail RCF at more than one point of each rail cross-section for the same circulation.  
Different kinds of vehicles running on railway tracks can be modeled with MBS software. In addition to the vehicle, the track system is also modeled with MBS software. Measurement vehicles obtain wide information about the status of the track, providing a set of parameters/values related to each measured local point along the track, with linear step increments of a few centimeters. All these data can be divided into two main groups: those providing information about track geometry and those that correspond to track irregularities.  
Once the vehicle and the track section are modeled, the wheel-rail contact becomes of great importance. To guarantee the accuracy of the results, the real wheel and rail profiles are introduced into the model, what is achieved by means of specific format files that contain the shape of these profiles using different coordinate points. To solve the contact problem in normal and tangential directions, based on the nonlinear [PERSON] and [PERSON]'s theories respectively, FASTSIM algorithm [33] is used. This algorithm is the numerical implementation of [PERSON]'s simplified theory [34] which is commonly used for wheel-rail wear calculations [35]. For each wheel-rail contact, FASTSIM is evaluated with constant normal forces which nature is influenced by wheel and rail profiles. It is a key point that the selected MBS software is capable of taking into account all the possible contact patches between wheel and rail. Creepages are obtained as well; creepage is a non-dimensional parameter defined as the relative velocity between wheel and rail normalized by the rolling velocity.  
The definition of the operation conditions is also important to obtain better results. The friction coefficient plays an important role in the vehicle-track interaction [36]. If either rail or flange lubrication is used, the multibody model can be adapted to change the friction value for different positions of the contact along the track. The way the speed is modeled is also important since the trains stop at stations and must adapt to speed commands and limits. The speed profile of the trains, along with the vertical track profile and load condition, impose a variable torque on the wheelsets for traction and braking operations.  
When the simulation process has finished, some post-processing of the results (e.g., load and creepage values among others) is necessary. Then, the desired parameters are organized in a structured way, regarding the type of the result, wheelset, trackside, and/or the number of contact patches. These parameters will be the inputs for the rail RCF module (and eventually other degradation modules) and are left constant within each time step (\(\Delta t\)). The capabilities of the described MBS has proven suitable to provide the inputs that are necessary for the different crack prediction models.