Thermomechanical coupling

Many mechanical parts are subject to both mechanical and thermal stress. This is the case, for example, of turbine blades subjected to high temperatures and inertial forces, or of a forged part that heats up when deformed. Simulating such problems may require solving both a thermal problem (determining the temperature field in the blade) and a mechanical problem (determining the stress in the blade).

In some cases, these two problems are linked. For example, when a part is heated, it expands and deforms. If the part cannot deform freely, stress is created. Thermal stress causes mechanical strain or deformation. On the contrary, if a metallic material is strongly deformed, it heats up. Mechanical stress then generates a thermal effect. Mechanical and thermal problems are said to be coupled, and we speak of thermomechanical coupling.

The first objective of this article is to determine the equations governing these two problems and to demonstrate their coupling. The second objective is to give some examples of the application of thermomechanical coupling.

In this article, we shall confine ourselves to the study of volume thermomechanical phenomena, and in particular we shall not consider the thermomechanical coupling involved in friction between solids. To determine the thermomechanical equations, we will always assume small deformations.