Thermodynamics and solution methods for coupled problems

In this chapter we study one of the most important examples of multi-physics problems, the coupling between mechanics and heat transfer that is naturally placed within the thermodynamics framework. All the model problems selected herein for illustration of thermodynamical coupling are non-stationary. We start by revisiting the initial-boundary value problem in elastodynamics for both small and large strain case. We then turn to inelastic problems, with plasticity model first, and then finally to contact. For each of the chosen model problems, we will underline the changes which are brought by taking into account the thermodynamical coupling, such as the temperature dependence of mechanical properties. More importantly, we will present for each problem how to construct the corresponding operator split solution method, which combines the finite element solution procedure already presented for non-stationary heat transfer on one hand with the corresponding solution method for mechanics problem on the other.