Towards a framework for non-linear thermal models in shell domains

Coupled thermal models defined in degenerated domains, like plates or shells, in- volve many numerical difficulties. First, such models are non-linear because the de- pendence of model parameters explicitly or implicitly on the temperature field and because the presence of terms expressing the thermo-mechanics or thermo-chemical couplings. Second, the resulting transient models usually involve many and very different characteristic times. Third, such models are many times defined in degen- erated domains which contain at least one of its characteristic dimensions much smaller that the others ones, and in such geometries it is well known that 3D fully solutions remain difficult because the extremely fine meshes needed for describing the evolution of the different fields in the smallest dimensions. Finally, sometimes real time simulations are envisaged, and in that case one could envisage the off-line construction of parametric solutions to be employed on-line for real-time control purposes. In this work we propose a framework able to address the just mentioned issues which implies the combination of non-incremental parametric separated rep- resentations within the PGD framework, the separation of the physical spaces for circumventing the issues related to degenerated geometries and the asymptotic nu- merical method for addressing the solution of coupled non-linear parametric models.