In-plane/out-of-plane separated representations of updated Lagrangian descriptions of viscoplastic flow models in plate domains

A new efficient updated Lagrangian strategy for numerical simulations of material forming processes is presented. The basic ingredient is the tensorial decomposition of the velocity field into a finite sum of in-plane and an out-of-plane components, giving rise to an equivalent computational complexity of some two-dimensional problems and some one-dimensional ones (therefore, much less than the true three-dimensional complexity of the original problem). This is efficiently achieved by using Proper Generalized Decomposition (PGD) techniques, which are here employed in an updated Lagrangian framework for the very first time. This updated Lagrangian nature of the method needs the use of a robust numerical integration technique (in this case, the Stabilized Conforming Nodal Integration has been chosen) for addressing the highly distorted projected meshes. The resulting strategy is of general purpose, although it is especially well suited for addressing models defined in plate or shell (in general, parallelepipedic) domains. The basics of the just-developed method are shown, together with some numerical examples to show the potential of the technique.