Then, to solve the contact problem of inhomogeneous materials, a semianalytic solution for inhomogeneous inclusions with arbitrary shape in an isotropic half space under contact loading through the EIM was proposed by Zhou et al.

The heterogeneous particles distributed in the matrix can be described as a domain that has the same material properties as the matrix but with eigenstrains (proposed by Mura) through the equivalent inclusion method (EIM) proposed by Eshelby. The contact components with inhomogeneities have been investigated by many researchers. Therefore, it is meaningful to study EHL with particles on rough contact surfaces to observe the behavior of the lubrication process and improve the lubrication environment. In addition, the inhomogeneity can change the elastic field of the matrix, and then the film thickness and pressure of the EHL will be affected by the particles indirectly. However, in reality, the contact surfaces of the mechanical components are usually rough, and surface roughness is one of the important factors that cause failure of the lubrication film in EHL contact. Most studies of EHL with inhomogeneous materials are usually carried out on smooth surfaces. Elastohydrodynamic lubrication (EHL) is a common theory to explain the problem of surface deformation and rheological characteristics under working conditions. The improvement in working load of mechanical components is a major challenge for the development of sophisticated equipment. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study.

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