Microscopic design and optimization of hydrodynamically lubricated dissipative interfaces

A homogenization‐based topology optimization framework is developed, which can endow hydrodynamically lubricated interfaces with a micro‐texture, to achieve optimal macroscopic responses by addressing both dissipative and nondissipative physics at the interface. With respect to the homogenization aspects of the problem, the thermodynamic consistency of the two‐scale formulation is explicitly analyzed and verified. With respect to the topology optimization aspects, a variational approach to sensitivity analysis is pursued. Subsequently, these are employed in micro‐texture design studies, which address microscopic and macroscopic objectives. The influence of dissipation on the optimization results is demonstrated through extensive numerical investigations, which also highlight the importance of working in a sufficiently flexible design space that can deliver nearly optimal micro‐texture geometries.