The construction and operation of road infrastructure is currently facing enormous challenges: steadily increasing traffic volume, climate change, necessary maintenance work, increasingly autonomous traffic etc. At the same time, technical innovations (e.g. digitization, use of sensors, Industry 4.0) are rarely included into the road infrastructure so far. In order to enable a more sustainable, safer and more efficient construction and operation of roads in the future, a digital twin for the road of the future is under development in the Collaborative Research Center/Transregio 339. One key aspect for a digital twin of the road are realistic and at the same time efficient simulation models for the coupled vehicle-tire-pavement system as counterpart to the real road system (real twin). This contribution focusses on the thermo-mechanical representation of pavement structures loaded by rolling tires in order to investigate and predict its structural behavior. Finite strain asphalt material models are implemented into a finite element pavement model, which bases on an Arbitrary Lagrangian-Eulerian (ALE) formulation. The ALE formulation introduces a reference frame that moves with the tire through the space. In case of steady state rolling tires and a pavement, which is homogeneous in driving direction, the deformation state of the tire and the pavement with respect to the introduced moving ALE reference frame becomes time-independent. This feature enables a numerically efficient description of the tire-pavement interaction. However, due to acceleration, breaking and vehicle dynamics, the tire rolling conditions are often dynamic. To consider these load cases as well, a dynamic ALE formulation is developed that saves still numerical cost compared to a standard transient Lagrangian computation.