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The important gradients of stress arising in rough mechanical contacts due to interaction at the asperity level are responsible for damage mechanisms like rolling contact fatigue, wear, or crack propagation. The deterministic approach to this process requires computationally effective numerical solutions, capable of handling very fine meshes that capture the particular features of the investigated contacting surface. The spatial discretization needs to be supported by temporal sampling of the simulation window when time-dependent viscoelastic constitutive laws are considered in the description of the material response. Moreover, when real surface microtopography is considered, steep slopes inevitably lead to localized plastic deformation at the tip of the asperities that are first brought into contact. A computer model for the rough contact of linear viscoelastic materials, capable of handling deterministic contact geometry, complex viscoelastic models, and arbitrary loading histories, is advanced in this paper. Plasticity is considered in a simplified manner that preserves the information regarding the contact area and the pressure distribution without computing the residual strains and stresses. The model is expected to predict the contact behavior of deterministic rough surfaces as resulting from practical engineering applications, thus assisting the design of durable machine elements using elastomers or rubbers

Modelling of Rough Contact between Linear Viscoelastic Materials