Two-scale homogenization study of a Reynolds-rod elastohydrodynamic model

In this paper, the existence of solution for a coupled system of variational inequalities with highly oscillating coefficients modelling a micro-elastohydrodynamic lubrica tion problem is stated. Moreover, by means of two-scale convergence techniques, the limit coupled models when the frequency of oscillation tends to zero are established for different amplitude-frequency rates. The effect of roughness appears to be limited to one of the coupled nonlinear equations, either the elastic one or the hydrodynamic one. Finally, some numerical examples to illustrate both the qualitative behavior of the solution and the theoretical convergence results are presented.