This article presents an investigation of frictional shakedown for layered systems subjected to periodic contact loading. The term shakedown is here referred to as the possibility of developing interfacial residual stresses at the layer/substrate interface such that frictional slip, originally activated by the applied external contact load, ceases after a few loading cycles. The two-dimensional elastic problem of an elastic strip uniformly pressed against an elastic half-plane and subjected to a concentrated oscillating tangential force is studied. A quadratic programming technique which enables to resolve interfacial micro-slip adopting the distributed dislocation technique is proposed to analyse the behaviour at the layer/substrate interface. The solution to the problem is first validated against classical solutions and subsequently used to map the interfacial behaviour of layered systems undergoing different loading scenarios.

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