We study the transient contact of two sliding bodies with a simple geometry. The model employs the Archard law of wear in which the rate of material removal is proportional to pressure and speed of sliding. The problem is formulated in terms of two governing equations with unknown pressure and heat flux at the interface. The equations are solved numerically, using appropriately chosen Green’s functions. We start with a single area of contact. As a result of frictional heating and thermal expansion, the contact area shrinks, which leads to further localization of pressure and temperature. The role of wear is twofold. By removing protruding portions of the two bodies, wear tends to smoothen out pressure and temperature. On the other hand, it causes the contact area to grow sufficiently large to become unstable and bifurcate. Areas carrying load are eventually removed by wear, and the contact moves elsewhere. The system develops a cyclic behavior in which contact and non-contact areas interchange.

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