Mixed finite element formulations with volume bubble functions for triangular elements

This paper deals with volume bubble functions for mixed finite triangular elements in geometrically linear elasticity. In two different versions these functions are used in order to enrich the displacement field and the enhanced strain field, respectively. Appropriate conditions for satisfaction of the patch test are verified. In the numerical example, firstly the patch test is satisfied. Secondly, simulations of Cook’s membrane problem demonstrate that the proposed formulations avoid locking and reduce stress oscillations for incompressible materials.