We review recent developments in the response to periodic loading of elastic systems with frictional interfaces. The steady state can involve shakedown (no slip at any point), cyclic microslip leading to energy dissipation and possible fretting damage, or ratchetting (relative rigid-body motion accumulating during each cycle). Shakedown theorems can be established for systems in which the normal and tangential problems are uncoupled, but for coupled systems, the steady state depends on the initial conditions. In such cases the system ‘memory’ resides in the slip displacements at permanently stuck nodes. Analytical and asymptotic (continuum) methods for solving cyclic slip problems are also discussed.
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