<p>This work presents a novel contact formulation for two-dimensional bodies based on the penalty method. The proposed algorithm directly computes the overlapping area between the perimeters of the master and slave bodies. Contact detection is performed efficiently through a geometric collision test, and the contact force is evaluated proportionally to the intersection area. The direction of the contact force is evaluated using weighted distances related to the nodal indentation. This formulation can be used for both rigid and flexible bodies. In the latter, the global contact force is further decomposed into the nodal forces following specific assumptions. The methodology is first validated by comparing results obtained using the well-established segment-to-segment (STS) penalty formulation. Then, five numerical simulations, including a planar pin-joint mechanism, a standard patch test, a cam-follower system, a Geneva mechanism, and a falling body are studied to demonstrate the efficiency of the proposed method.</p>