A generalized Newton method for contact problems with friction. (English) Zbl 0679.73046

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.


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