A Hu-Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics

An original, variational formulation of the Virtual Element Method (VEM) is proposed, based on a Hu-Washizu mixed variational statement for 2D linear elastostatics. The proposed variational framework appears to be ideal for the formulation of VEs, whereby compatibility is enforced in a weak sense and the strain model can be prescribed a priori, independently of the unknown displacement model. It is shown how the ensuing freedom in the definition of the strain model can be conveniently exploited for the formulation of self-stabilized and possibly locking-free low order VEs. The superior performances of the VEs formulated within this framework has been verified by application to several numerical tests.

Automated summary

An original variational formulation of the Virtual Element Method (VEM) based on a Hu-Washizu mixed variational statement for 2D linear elastostatics is proposed. The proposed framework allows for weak enforcement of compatibility and independent prescription of the strain model, giving freedom in formulation of self-stabilized and possibly locking-free low order VEs. The superior performance of the VEs formulated within this framework is verified through several numerical tests.