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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.

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
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