A semi-analytic solution is presented for multiple inhomogeneous inclusions and cracks in a half-space under elastohydrodynamic lubrication contact. In formulating the governing equations, each inhomogeneous inclusion embedded under the contacting surfaces is modeled as a homogeneous inclusion with initial eigenstrains plus unknown equivalent eigenstrains by employing Eshelby's equivalent inclusion method, while each crack of mixed modes I and II is treated as a distribution of climb and glide dislocations with unknown densities according to the dislocation distribution technique. Such a treatment converts the problem into a homogeneous lubricated contact with disturbed deformation due to the inclusions and cracks. The unknowns in the governing equations are integrated by a numerical algorithm and determined iteratively by utilizing a modified conjugate gradient method. The iterative process is performed until the convergence of the half-space surface displacements, which involve the displacements due to the inhomogeneous inclusions and cracks as well as the fluid pressure. Samples are presented to demonstrate the generality of the solution.

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In order to predict the microscopic response of surface coatings and subsurface inhomogeneous inclusions, a semianalytical solution is developed for heterogeneous materials subjected to elastohydrodynamic lubrication contact. In this solution, the inhomogeneous inclusions are homogenized according to Eshelby's equivalent inclusion method with unknown eigenstrains to be determined. The topmost coating is assumed as an inhomogeneous inclusion of finite size and thus simulated with the same methodology. The disturbed surface deformation due to the presence of coatings and inhomogeneous inclusions are iteratively introduced into the lubricant film thickness until a convergence is achieved. The effects of surface roughness on the pressure and film thickness profiles and subsurface elastic fields are considered to approach the engineering practice. This solution takes into account the interactions between the loading body, the fluid lubricant and the coating/substrate system with embedded inclusions.

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