New models to accurately manage incompressibility with finite strain and every constitutive law

by D. Al-Akhrass, PhD student EDF R & D / AMA and École des Mines de Saint-Étienne, S. Fayolle EDF R & D / AMA

During the last months, we have worked on the development of a new way to deal with incompressibility with finite strain. Our main goals were:

1. to use the model with GDEF_LOG finite strain formalism which is compatible with each of Code_Aster’s constitutive law,
2. to have an accurate and generic methods which exclude EAS method or sub-selective integration.

Therefore, we choose to work on a three fields mixed finite element formulation (displacement, volumetric strain, pressure). The introduction of this formulation in Code_Aster results in three new modelisations: 3D_INCO_LOG, D_PLAN_INCO_LOG and AXIS_INCO_LOG.

This work is a report of the EDF project entitled Advanced Numerical Methods in Mechanical Engineering. It has led to this presentation in an international conference :
"Stabilized finite element methods to deal with incompressibility in solid mechanics in finite strains", D. Al Akhrass, S. Drapier, J. Bruchon, and S. Fayolle, European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria, 2012.

Work on this topic will continue with the development of capabilities for dynamic calculations, performance improvement, the implementation of stabilizing elements to use linear interpolation for displacement and the development of two fields mixed element formulations for J2 type plasticity laws.

The animation below shows the equivalent von Mises stress during indentation of a billet of steel. Contact with the upper and lower tools is managed by CONTINUE method with the algorithm of generalized Newton.