Stabilized mixed triangular elements with area bubble functions at small and large deformations

A well known approach for stabilization of mixed finite triangular elements are volume bubble functions. In this paper a new concept of area bubble functions in geometrically linear (elastic and elasto-plastic) and geometrically non-linear elastic regimes is presented. These functions are used in order to enrich the displacement field. In the numerical examples, simulations for Cook's membrane problem and a block under central pressure demonstrate, that the proposed formulation avoids locking and reduces stress oscillations for incompressible materials. Furthermore, the results reveal that area bubble functions are superior to volume bubble functions. This paper is an extension of the works published by the authors regarding tetrahedral elements.