Computational Modelling of Thermomechanical Phenomena

"Many industrial processes involve materials that are subject to temperature change and thermal stress. Examples range from the casting of large metallic products to the cooling and reliability of small electronic components. Thermally induced stress is a major concern as it can lead to material damage and product failure. Material properties, thermal and mechanical, and process conditions such as the size and location of a feeder in metals casting, or the power dissipation in a computer chip, will govern the magnitude of these stresses. Temperature may also be influenced by fluid flow, for example, the airflow over a computer chip in a laptop will govern the rate of heat extraction, hence the temperature gradients in the chip and the evolving thermal stresses.This paper provides details on the governing equations for heat transfer (temperature) and solid mechanics (stress), their degree of coupling, and the numerical techniques used to solve them. Three examples are discussed to illustrate the use thermomechanical modelling. These also provide an insight into the degree of coupling required between the equations. The first example, involves thermal cycling of electronic components where a prescribed temperature field is applied. As temperature is known, this example only requires the solution of the stress equation. The second example also involves the modelling of an electronic component where the temperature field is also calculated. In both of these examples, the stress calculation is dependent on the temperature field, but the temperature calculation is not dependent of the solution of the stress equation (one-way coupling). The final example provides details on modelling the metals casting process. Both the temperature and stress equations are solved but, unlike the previous two examples, in this case the temperature field is dependent on the results from the stress calculation (two-way coupling)."