## 1 Introduction
Because damage originates in the contact patch, the contact mechanics within the contact patch must be examined to better understand the damage mechanisms. Because dynamic wheel-rail contact is difficult to measure, a numerical analysis that can accurately simulate the vehicle-track dynamic interaction must be developed to analyze corrugation under controlled conditions [13]. The Hertzian treatment of the contact problem has usually been used to solve normal contact problems [9], whereas [PERSON]'s theories [14] are typically employed for the tangential direction [9]. The Hertzian solution considers that contact surfaces are frictionless smooth half-spaces. However, for worn or deformed profiles, such surface approximations may not hold in the vicinity of the contact patch [15; 16]. [PERSON] [16] employed a two-dimensional (2D) non-Hertzian contact model and found that the shape of the normal stress distribution was not elliptic because of the geometrical asymmetry. Correspondingly, the tangential stress distribution varies along different positions of the corrugation and may be responsible for the development of corrugation. In addition, the Hertzian theory and [PERSON]'s theory are based on statics. However, because the contact patch is on the order of 2 cm, which is similar to the corrugation wavelength, non-steady state processes caused by dynamic interactions must be considered [17; 18]. In addition to long-term damage mechanisms, a short-term dynamic process is believed to fix the wavelength through structural dynamics [1; 19]. The interaction between the short- and long-term mechanisms is represented by a feedback loop [1]. Three phenomena must be defined to understand corrugation development: (1) structural dynamics excitation caused by vehicle-track interactions, (2) loading response at the wheel-rail interface involving contact mechanics and (3) feedback from the contact and damage to the structural dynamics as determined by the direct coupling between the contact mechanics and structural dynamics. In [9; 20], a crucial understanding of the contact phenomena in the corrugation problem is provided. The model used in [9; 20] solved the structural dynamics and contact mechanics problems separately in different models or steps. In addition to a more elaborated treatment of the contact mechanics and an accurate representation of the vehicle-track interaction, we propose a combined modeling approach that includes the coupling and interplay of both the structural dynamics and contact mechanics problems. This solution is inspired by the work of [9] and the question \"why is roughness growth predicted by a simple contact model but not when complexity is increased to include non-Hertzian and non-steady contact conditions?\"  
The finite element method has been employed to investigate the development mechanism underlying squats in a vehicle-track system [7]. This modeling approach provides a good explanation for the development of corrugation initiated from isolated known railhead irregularities [21]. Because corrugation from isolated known railhead irregularities is of a short pitch type, this method could also be valid for investigating general types of short pitch corrugation. Corrugation that originates from railhead irregularities is caused by a dynamic force excited by known irregularities. In this case, the wavelength of the force is determined by the local track system, and the phase of the force is determined by the location of the irregularities. Thus, clear mechanisms of wavelength and phase fixing are involved. The wavelength and phase of the force at a given irregularity are always the same. Consequently, the resulting differential wear and/or plastic deformation is always in phase and damage accumulates under different wheel passages. In this way, corrugation can initiate and grow. In the case of the general type of short pitch corrugation, a visually-identifiable initiation source is not observed.