Stabilized mixed triangular finite elements at large deformations using area bubble functions

Abstract

AbstractIn this paper stabilized mixed triangular finite elements are presented in order to avoid volume locking and to damp stress oscillations. Geometrically non‐linear elastic problems are addressed. The mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases. As a key idea, volume and area bubble functions are used for the method of incompatible modes and the enhanced strain method [1], thus giving both the interpretation of a mixed finite element method with stabilization terms. Concerning non‐linear problems these are non‐linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used [1]. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two‐field method, the method of incompatible modes and the enhanced strain method in finite deformation problems is derived for a hyper elastic Neo‐Hookean material. In the representative example Cook's membrane problem illustrates the good performance of the presented approaches compared to existing finite element formulations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)