A weighted Nitsche stabilized method for small-sliding contact on frictional surfaces

We propose a weighted Nitsche framework for small-sliding frictional contact problems on three-dimensional interfaces. The proposed method inherits the advantages of both augmented Lagrange multiplier and penalty methods while also addressing their shortcomings. Algorithmic details of the traction update and consistent linearization in the presence of Nitsche terms are provided. Several benchmark numerical experiments are conducted and the results are compared with existing studies. The results are encouraging and indicate accurate satisfaction of the non-interpenetration constraint, stable tractions and asymptotic quadratic convergence of the Newton-Raphson method.