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In this paper, modelling methods are developed to achieve dynamics exploration for the vehicle–track system and its substructures. First, a coupled model, with the satisfaction of wheel–rail displacement compatibility and force equilibrium within each time step, is constructed for the characterisation of vehicle–track interaction, where the vehicle is modelled as a multi-rigid-body system, the ballasted tracks are modelled as a combination of elasticity, damping and mass structures by finite-element method, and time-varying wheel–rail contacts in geometry, creep and force are depicted at the three-dimensional space. On the foundation of vehicle–track interactions, a multi-finite-element coupling method originated from the energy variation principle is presented to integrate multiple substructures, such as bridge and soil subgrade, into the vehicle–track coupled system. Due to the variation of dominant frequencies of the vehicle–track system and its substructures, a multi-time-step solution method is proposed to achieve a hybrid solution of fine and coarse time step size for the vehicle–track system and substructure system, respectively. Numerical examples are presented to show the accuracy and practicality of the proposed model and methods.

Modelling of vehicle-track related dynamics: a development of multi-finite-element coupling method and multi-time-step solution method