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In the frictional contact of solids under cyclic loads, the shakedown behaviour of the relative displacement is of interest in the same spirit as the plastic deformation in plasticity. Cumulative slips may lead to the failure due to large relative displacements of the components of an assembly while cyclic slips are often undesired because of wear and fretting÷fatigue problems. Under Coulomb friction, it is well known that Melan and Koiter theorems are generally not available, except in certain particular cases. In this discussion, the particular case of small coupling between the contact pressures and the slip-displacements is considered. This assumption means that the tangent displacements have small or no influence on the contact pressures which can be then computed from the elastic response as in the uncoupling case. The pressure is thus a given time-dependent function and the Coulomb criterion is reduced to a Mises-like standard law of friction. It is shown here that Melan and Koiter theorems can be applied again as in standard plasticity. The dependence of the yield limit on the loading amplitude is however not classical and the extension of the static and kinematic approaches is discussed to obtain the critical shakedown load or the limit load. The validity of the assumption of small coupling is also explored by numerical simulation in a practical example.

Slip-shakedown analysis and the assumption of small coupling in frictional contact