Wear of a cylindrical punch composed by two different materials alternatively distributed in annular forms is studied with the method of dimensionality reduction (MDR). The changes in surface topography and pressure distribution during the wear process is obtained and validated by the boundary element method (BEM). The pressure in each annular ring approaches a constant in a stationary state where the surface topography does not change any more. Furthermore, in an easier manner, using direct

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... egration, the limiting profile in a steady wear state is theoretically calculated, as well as the root mean square (RMS) of its surface gradient, which is closely related to the coefficient of friction between this kind of surface and an elastomer. The dependence on the wear coefficients and the width of the annular areas of two phases is obtained.