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On the general rolling contact problem for finite deformations of a viscoelastic cylinder. (English) Zbl 0582.73113
The formulation of a variational principle for the finite steady-state deformation of a rolling cylinder is presented together with finite element methods and numerical algorithms for the analysis of such problems. The unilateral contact of hyperelastic and viscoelastic rolling cylinders on a rough foundation on which nonclassical friction laws hold is characterized by a highly nonlinear variational inequality, the solutions of which can exhibit bifurcations for certain values of angular velocity. Some of these bifurcations correspond to the emergence of standing waves in such cylinders. The results of several numerical experiments are also presented.

MSC:
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74B20 Nonlinear elasticity
74S05 Finite element methods applied to problems in solid mechanics
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
49J40 Variational inequalities
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