## 6 Conclusions and Future Work  
In this paper, the enigma of rail short pitch corrugation is examined using a novel modeling approach. Although the enigma remains unsolved, new insights on the phenomenon are described. The approach consists of simulating the vehicle-track dynamic interactions, which are directly and instantaneous coupled through frictional rolling contact. Wear is assumed to be the damage mechanism. The wheel, track and contact are treated in three dimensions so that the structural, geometric and material properties of the system and its components can be modeled sufficiently. The analysis concentrates on the transient rolling at the corrugation and the behavior of the vehicle-track system under the rapid oscillating loading of Dutch railway track and traffic in an effort to identify the preferred conditions under which corrugation can consistently initiate and grow. The findings and insights are summarized as follows. Along the longitudinal centerline of the contact patch, increases in the contact area, maximum pressure, shear stress and micro-slips at the corrugation crest are small, and some of them even decrease with increases in the corrugation amplitude. However, changes at the trough are large. The large micro-slip and the significantly reduced contact pressure at the trough are the major contributions to the differential wear, which causes corrugation initiation and growth. The dependence of the normal contact force on corrugation excitation is strong, and the dependence of the longitudinal contact force on excitation is relatively weak. In addition to the commonly-accepted hypothesis for corrugation studies, i.e., the vertical vibration modes of the vehicle-track system determine the development of corrugation, it is found that the longitudinal vibration modes are also important. Longitudinal modes are likely to be important for the initiation of corrugation, and when the corrugation amplitude is sufficiently large, the vertical modes will be dominant. For intermediate situations, the longitudinal and vertical modes together determine whether the corrugation will grow or be suppressed by wear depending on whether the wear is of the necessary consistent frequency and phase. The main frequencies of the vertical and longitudinal vibration modes and contact forces, as well as the resulting wear are different. Consequently, a condition (that might not be unique) for corrugation to consistently initiate and grow should be that the longitudinal and vertical main frequencies are consistent. This consistency may be achieved by the control of certain track parameters, for instance by properly constraining the rail fastening. The modeling and findings agree with field observations (Figure 1) of the distribution of corrugation with different severities. The proposed modeling is promising for corrugation analyses. Future work may include identifying the track parameters required for the system to converge to the preferred frequencies and wavelengths and investigating the phase-fixing mechanism of wear that promotes corrugation growth at every wheel passage. To this end, the first focus should be on rail fastening. Previous work has shown that the fastening system, including the rail pads, has a strong influence on the vertical and longitudinal dynamics. This research is partly supported by ProRail and by NeTIRail-INFRA (Needs Tailored Interoperable Railway project focused on infrastructure), an EU Horizon 2020 program for research and innovation (Project No. 636237), as well as by an open call project of the Key Laboratory of Theory and Technology of High-Speed Railway Structures, Ministry of Education of China, Southwest Jiaotong University (Project No. 2014-HRE-03). [PERSON] and [PERSON] conceived and designed the idea and numerical study; [PERSON] performed the numerical study; [PERSON], [PERSON], [PERSON] and [PERSON] analyzed the data and contributed in writing the paper; [PERSON] and [PERSON] contributed in obtaining the funding for performing the research.