Contact problem is one of the common non-linear problems. How to simulate the deformation and strength characteristics of the contact surface and realize the real simulation of the contact problem between deformers is a difficult problem in this field. Based on the physical meaning of the 2D (2 dimensional) contact problems

their equivalent complementary models are established in normal and tangential directions respectively. Then a system of non-smooth equations is employed to describe the complementary models by Fischer-Burmeister (FB) function in the NCP function

which can be solved by the conventional Newton algorithm. In addition

good accuracy of the solution can be obtained by a small number of integration points based on the Gauss integration. In order to improve its accuracy and remove its discontinuity

a procedure of the contact surface at the Gauss point is employed in the surface-to-surface contact model

in which the accuracy of the solution can be controlled by adjusting the number of integration points. The procedure is easy to understand and convenient to implement. Based on this

a 2D contact finite element model is established

and the feasibility and effectiveness of the method are verified by some engineering examples. The results show that the proposed procedure has a higher accuracy and more realistic reflection of the actual problem than ABAQUS finite element method.