A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: Single interface

• Developed a weighted Nitsche stabilized method for frictional contact on embedded interfaces.
• Provided an optimal choice of weights for the weighted stress operator in the variational form.
• Provided an analytical estimate for the method parameter for lower order elements.
• Several numerical examples demonstrate the advantages of the method over traditional penalty and classical Nitsches method.

We investigate a finite element method for frictional sliding along embedded interfaces within a weighted Nitsche framework. For such problems, the proposed Nitsche stabilized approach combines the attractive features of two traditionally used approaches: viz. penalty methods and augmented Lagrange multiplier methods. In contrast to an augmented Lagrange multiplier method, the proposed approach is primal; this allows us to eliminate an outer augmentation loop as well as additional degrees of freedom. At the same time, in contrast to the penalty method, the proposed method is variationally consistent; this results in a stronger enforcement of the non-interpenetrability constraint. The method parameter arising in the proposed stabilized formulation is defined analytically, for lower order elements, through numerical analysis. This provides the proposed approach with greater robustness over both traditional penalty and augmented Lagrangian frameworks. Through this analytical estimate, we also demonstrate that the proposed choice of weights, in the weighted Nitsche framework, is indeed the optimal one. We validate the proposed approach through several benchmark numerical experiments.