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Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule. (English) Zbl 1072.74060

Summary: This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non-associated. The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non-associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi-axes ratio. The frictional contact law and its inverse are derived from a single non-differentiable scalar-valued function, called a bi-potential. The convexity properties of the bi-potential permit to associate stationary principles with initial-boundary value problems. With the present formulation, the time integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor-corrector step addresses all cases (sticking, sliding, no-contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
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