Real Time Simulation of Non-Linear Solids by PGD Techniques

We analyse here how Dynamic Data Driven Application Systems (DDDAS) can constitute a valuable tool in the field of forming processes. Simulation tools in the field of DDDAS are required to provide a response in real-time, a requisite that is often too severe for complex problems. Here, we consider that of hyperelasticity, commonly used in different fields such as rubber manufacturing or surgery, for instance. We analyse here how model reduction techniques, and particularly Proper Generalized Decompositions (PGD) methods can provide a suitable response to the strong requirements posed by DDDAS. We will consider two different approaches to the problem. The first one is an explicit approach that nevertheless provides with good results. The second one is based on the use of Asymptotic Numerical Method.