A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for pure traction problems of linear elasticity

We develop a lowest-order nonconforming virtual element method for planar linear elasticity in the pure traction formulation, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method, with the family of polygonal meshes satisfying a very general geometric assumption. A discrete Korn's inequality is established. And the method is shown to be uniformly convergent for the nearly incompressible case with an optimal convergence rate.