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Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2004
auteur(s) Hjiaj Mohammed; Feng Z.Q.; De Saxce Géry; Mroz Zénon
journal (abréviation) International Journal for Numerical Methods in Engineering (Int J Numer Meth Eng)
volume (numéro) 60 (12)
pages 2045 – 2076
résumé 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.
mots clés anisotropic friction condition • non-associated sliding rule • variational formulation • bi-potential • time stepping • augmented Lagrangian technique
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