A semi-analytical model (SAM) to tackle the steady-state elastic frictional rolling contact problem involving composites is presented. Specifically, the frictional rolling contact is categorized into two subtypes, namely normal and tangential problems, and the conjugate gradient method (CGM) is used to figure out the normal pressure and tangential traction. In SAM, the equivalent inclusion method (EIM) is applied to analyze the influence of composites on the matrix, and the displacement disturbance resulting from such composites is added to the total surface displacement, which implements the coupling between surface contact and composites. The accuracy of the proposed model is verified by the finite element model. The effects of composites on the frictional rolling contact behavior are investigated. The results indicate that Young's modulus, as well as the size and location of the composites, are correlated with the distributions of tangential traction, subsurface stresses and the sizes of stick and sliding zones.

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