A deformation dependent stabilization technique, exemplified by EAS elements at large strains

Stabilized finite element methods have been developed mainly in the context of Computational Fluid Dynamics (CFD) and have shown to be able to add sta bility to previously unstable formulations in a consistent way. In this con tribution a deformation dependent stabilization technique, conceptually bas ed on the above mentioned developments in the CFD area, is developed for So lid Mechanics to cure the well-known enhanced assumed strain (EAS) method f rom artificial instabilities (hourglass modes) that have been observed in t he range of large compressive strains. In investigating the defect of the original formulation the dominating role of the kinematic equation as cause for the instabilities is revealed. This observation serves as key ingredient for the design of the stabilizing ter m, introduced on the level of the variational equation. A proper design for the stabilization parameter is given based on a mechanical interpretation of the underlying defect as well as of the stabilizing action. This stabili zing action can be thought of an additional constraint, introduced into the reparametrized Hu-Washizu functional in a least-square form, together with a deformation dependent stabilization parameter. Numerical examples show t he capability of this approach to effectively eliminate spurious hourglass modes, which otherwise may appear in the presence of large compressive stra ins, while preserving the advantageous features of the EAS method, namely t he reduction of the stiffness for an 'in-plane bending' mode, i.e. when pla ne stress elements are used in a bending situation. (C) 2000 Elsevier Scien ce S.A. All rights reserved.