A computational design framework for lubrication interfaces with active micro-textures

Abstract

The major goal of the present study is to develop a computational design framework for the active control of hydrodynamically lubricated interfaces. The framework ultimately delivers an electrode distribution on an elastomeric substrate such that a voltage-controlled texture may be induced on its surface. This enables the setup to attain a desired time-dependent macroscopic lubrication response. The computational framework is based on a numerically efficient two-stage design approach. In the first stage, a topology optimization framework is introduced for determining a microscopic texture and the uniform modulation of its amplitude. The objective is to attain the targeted fluid flux or frictional traction signals based on the homogenization-based macroscopic response of the texture. As a minor goal, a novel unit cell geometry optimization feature will be developed which will enable working in a design space that is as unrestricted as possible. The obtained designs are then transferred to the second stage where the electrode distribution on a soft substrate is determined along with the voltage variation that delivers the desired amplitude variation. The first stage operates in a two-dimensional setting based on the Reynolds equation whereas the second stage operates in a three-dimensional setting based on an electroelasticity formulation. The two stages are heuristically coupled by transferring the texture topology to the electrode distribution through a projection step. The viability of such an active lubrication interface design approach is demonstrated through numerous examples that methodically investigate the central features of the overall computational framework.