Simulation of Thermoelastic Problems with the Finite Element Method

Disc brakes convert kinetic energy into thermal energy in order to slow down vehicles. During the braking process enormous heat flows and temperature gradients occur in the system. Because heating leads to a change in shape for most materials, it is important to take the temperature and its influence into account during the design process. The interaction between the structure and the heat in disc brakes can be described with methods from thermoelasticity. To simulate thermoelastic behaviour the Finite Element Method is commonly used. The thermal and mechanical domain are taken into account by coupling the equation of motion and the heat equation. However, in transient analysis often the problem occurs of different time scales of the structural and thermal dynamics for many technically relevant materials, like steel. For metallic materials the time constant of structural dynamics is much smaller than those of thermal dynamics. This complicates an efficient transient simulation. In the present work the implementation of a Finite Element Method in thermoelasticity and associated investigations are shown. The method is applied to various parts and load cases. Also different approaches to deal with the different time scales will be shown. Heuristic methods like mass‐scaling as well as more mathematically oriented approaches like model order reduction are presented.