Locking-free nonconforming finite elements for planar linear elasticity

In this paper we introduce a nonconforming finite element method for a planar linear elasticity problem. We show that this nonconforming method is robust in that error estimates generated by it are uniform with respect to one of the Lame elasticity constants, $\l$; i.e., it is locking-free. Applications to nonconforming $P_1$ and rotated $Q_1$ finite elements are discussed.