  We design and analyse a Nitsche method for contact problems. Compared to the
seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact
problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method
is constructed by expressing the contact conditions in a nonlinear function for
the displacement variable instead of the lateral forces. The contact condition
is then imposed using the nonsymmetric variant of Nitsche's method that does
not require a penalty term for stability. Nonconforming piecewise affine
elements are considered for the bulk discretization. We prove optimal error
estimates in the energy norm.
