OSGS Finite Elements to deal with incompressibility in small strains

by D. Al-Akhrass and S. Fayolle, EDF R&D / AMA

In order to deal to incompressibility, one may resort to a hybrid finite element formulation. When working in small strains, Code_Aster lets the user choose between *_INCO, a three field approach (displacement, pressure, volumetric strain), and *_INCO_UP, a two field based model (displacement and pressure). Up to now, the latter was only available with triangles and tetrahedrons when working with linear elements (P1+/P1 element).

Thanks to a PhD thesis in partnership with Ecole des Mines de Saint-Étienne, the OSGS method was implemented to expand the scope of the *_INCO_UP model to all linear elements. The new method is called by applying *_INCO_OSGS models.

The following example is a comparison between second order and linear elements based on the OSGS method on an elasto-plastic piece (the trace of the stress tensor is shown).

Figure 1 : Trace of stress tensor at Gauss points in MPa : ( a ) tetrahedral element P2/P1, ( b ) tetrahedral element OSGS, ( c ) hexahedral element P2/P1, ( d ) hexahedral element OSGS.

Available in the 11.1.6 version and future releases