The design of modern structures is confronted with several challenges including: i) the exploitation at the macroscopic level of properties arising from the local microscopic substructures, ii) reliability assessment based upon the analysis of very large deformation states, iii) acceleration of the design process which implies high-performance and parallel computing. The talk will present a mathematical and numerical perspective regarding such questions.
Multi-scale analysis is very much related to domain decomposition methods, which are well known to suffer from highly heterogeneous behaviors and high geometrical aspect ratios. We will illustrate this link and will present major enhancements of the traditional methods (Schwarz, FETI) based upon the automatic construction of optimal coarse grids.
Large deformation contact dynamics always remain a field of active research. We will present contributions to the improved variational formulation of contact within implicit time integration schemes achieving good regularity and energy conservation properties.
Updated Lagragian procedures will also be presented, with specific constructions of deformation gradient fields exhibiting various convincing properties.
Such aspects will be illustrated on industrial cases from various areas, including tyre manufacturing.