Choice of the stress integration scheme for accurate large-deformation finite element analysis

The use of computational structural models that include geometrical non-linearity in many application cases may require high reliability in prediction of displacements. Nevertheless, large differences up to 60% on maximum total displacement have been found among results of static large-deformation analyses performed by means of the major commercial software packages in a simple benchmark study with linear material properties. In order to investigate the causes of such disagreement, the present work compares different finite element formulations including well-established stress update schemes. The various formulations are tested, and results are compared in three test cases. Rodriguez stress update algorithms have shown the best performance among methods reported in literature. Finally, the cause of the large differences found in the predictions of commercial codes is identified. It is linked to the energetic inconsistency of some stress update methods in the simulation of extension/compression loading conditions. Such inaccuracy is reproduced analytically by formulating and integrating the corresponding inconsistent constitutive equations. The identified problem is very important for designers, as it affects almost all the static simulations, which are the most common type of large-deformation analyses and usually involve extension/compression loading.