Curnier, A.; Alart, P. A generalized Newton method for contact problems with friction. (English) Zbl 0679.73046 J. Méc. Théor. Appl. 7, Suppl. 1, 67-82 (1988). Summary: This article reviews the numerical methods used for a few years in the program TACT to solve contact problems with non-associated Coulomb’s friction. These methods include: a penalty method to enforce the contact and adherence conditions respectively, an implicit projection method to integrate the slip rule, the finite element method for the spatial discretization and a generalized Newton method to overcome the contact and friction nonlinearities. Recent advances improving the robustness of the resulting frictional contact algorithm are reported. In particular, a necessary and sufficient condition on the friction coefficient for the solution to flat contacts to be unique is stated and a damping factor is introduced to guarantee the algorithm convergence to this solution in the two-dimensional case. The flat punch problem is used to illustrate both the accuracy and efficiency of the method. Cited in 42 Documents MSC: 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 74S05 Finite element methods applied to problems in solid mechanics Keywords:penalty method to enforce the contact and adherence conditions; implicit projection method to integrate the slip rule; finite element method for the spatial discretization; generalized Newton method; contact and friction nonlinearities; frictional contact algorithm; damping factor; convergence; two-dimensional case; flat punch problem PDFBibTeX XMLCite \textit{A. Curnier} and \textit{P. Alart}, J. Méc. Théor. Appl. 7, 67--82 (1988; Zbl 0679.73046)