## Real time simulation of forming processes by Proper Generalized Decomposition (PGD) methods

This page displays information about the project CICYT-DPI2011-27778-C01/02, funded by the Spanish Ministry of Education and Science. Scientific leader of the project: Elias Cueto

### Participants:

**Group of Applied Mechanics and Bioengineering. amb-I3A.**

Francisco Chinesta (GeM EC-Nantes)

**Laboratori de Calcul Numeric, UPC-BarcelonaTech. Lacan.**

Antonio Huerta, PI of the Lacan sub-project.

**Goals of the project:**

Decision taking in industrial contexts faces very often the problem of the cost associated with the nowadays very accurate, but very time consuming, simulation process. This project deals with the real-time simulation of forming processes. By that we mean a simulation that runs in a short time, enabling decision taking without the mentioned burden associated with traditional (say, FE, FV, FD, …) simulation techniques for complex forming processes. Model reduction techniques allow for the development of highly reduced models (in terms of a few degrees of freedom) that therefore induce a very limited computational cost. We consider in this project, in particular, a novel, state-of-the-art, technique of a priori model reduction coined as Proper Generalized Decomposition (PGD). This technique allows for the obtention of a priori reduced order models (in contrast with existing a posteriori techniques that need for a number of prior complete simulations whose results are treated in a statistical manner to obtain the relevant information needed in the reduced model). This technique allows to simulate a wide number of forming processes despite its youth, particularly some of industrial interest such as pultrusion, Resin Transfer Moulding or mould filling, for instance, by considering arbitrary values of the parameters of the system (filling pressure, temperatures in the oven, …) as additional coordinates of the model. One thus can think of “real-time post-processing” instead of “real-time simulation”. Pultrusion or RTM processes, for instance, are some natural candidates for this class of techniques. One can think, for instance, that through the employ of this technique, the engineer responsible of a certain equipment can be equipped with a smartphone, some of which allow for a non-negligible capability of calculation, that could allow for fast and simple, yet still accurate, simulations of the behavior of the industrial devices. This technique could eventually inform about the origin of some problems in the expected result of the forming processes, as will be demonstrated during the development of the project.

**Modeling forming processes on a PGD approach:**

This project is aimed at simulating some industrial forming processes such as pultrusion and RTM in a PGD approach.

PGD techniques allow for a physics-based meta-modeling approach to many problems without the ned for computer experiments. So to speak, it can be considered as an a priori model reduction tecnique.

**Mathematical basis of the PGD technique:**

The second big objective of this project is to fully understand and characterize the behaviour of PGD approach from a mathematical point of view: optimality, stability, …

**Some documentary simulations:**

You will find below a list of documentary films showing the performance of the technique:

Real-time simulation of elastic solids through PGD

Real-time simulation of surgery by PGD

Real-time simulation of surgery by PGD, another view

Parametric geometry simulated in real time.

Liver laparoscopy simulation with haptic feedback.

Interactive simulation of neo-Hookean beam bending on a tablet.