PGD in linear and nonlinear Computational Solid Mechanics

Mechanics continues to supply numerous science and engineering problems which remain inaccessible to standard FE codes. Not all these problems are exotic, and many are indeed practical problems. A significant number of these engineering challenges are related to the today’s growing interest in physics-based material models described on a scale smaller than that of the macroscopic structure, with applications such as structural design for which quasi real time simulation is mandatory. Design parameters and lacks of knowledge (variability, uncertainties) involving multiple parameters make these problems even more difficult.

This chapter addresses our answer to these computational challenges which is based on the Proper Generalized Decomposition (PGD) method that we have introduced in 1985 and developed until now. The two papers (Néron and Ladevèze, 2010; Chamoin et al., 2012) and the book (Ladevèze, 1996, 1999) are at the center of this chapter. Additions concern the main technical points which are detailed here for the first time.