The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

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