New routes to advanced simulation of material forming

Abstract

We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD), based on the assumption of a separated form of the unknown field. It has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. Many challenging problems can be efficiently cast into a multidimensional framework. For instance, parameters in a model (loads, initial conditions, boundary conditions, material parameters, geometrical parameters,...) can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort virtual chart. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, in highly complex scenarios and on deployed platforms.