The destabilization of the steady-state regime of two semi-infinite half-spaces of different elastic coefficients sliding upon each other has been theoretically investigated when a rate-and-state friction constitutive law controls the sliding. In the framework of linear and isotropic elastodynamics, the effect of the frictional constitutive law has been investigated onto the development of self-excited oscillations as well as the influence of the shear modulus difference between the two materials. The possibility of existence of a stick–slip regime and the conditions for the loss-of-contact are finally discussed.

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