A “soft” elastohydrodynamic lubrication model for a conformal one-dimensional sliding contact is presented. We describe surface-surface and fluid-surface interactions in conditions where asperities are in direct contact (mixed lubrication), and the effective film thickness is comparable in size to the roughness of the bounding surfaces. In the conditions considered, surfaces have a low elastic modulus, and fluid pressures have a low magnitude, relative to those found in most tribology applications. An interesting coupling is exhibited between the surface roughness, the global elasticity, and the fluid pressure. As opposed to typical tribological applications in conformal mixed lubrication contact, fluid pressure is strong enough to cause significant elastic displacement of the mean boundary surfaces. The deformation is taken into account in an iterative process to compute the resulting spatially dependent stresses, deformations and fluid pressures.

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