Computational framework for monolithic coupling for thin fluid flow in contact interfaces

Abstract

We develop a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range engineering, biological and geophysical applications. The treatment of this problem requires coupling between fluid and solid mechanics equations, further complicated by contact constraints and potentially complex geometrical features of contacting surfaces. We develop a monolithic finite-element framework for handling contact, thin incompressible viscous flow and fluid-induced tractions on the surface of the solid, suitable for both one-and two-way coupling approaches. Additionally, we consider fluid entrapment in "pools" delimited by contact patches and its pressurisation following a non-linear compressible constitutive law. Image analysis algorithms are adopted to identify the local status of each interface element (i.e. distinguish between contact, fluid flow and trapped fluid zones) within the Newton convergence loop. First, an application of the proposed framework for a problem with a model geometry is given, and the robustness is demonstrated by the DOF-wise and status-wise convergence. The full capability of the developed two-way coupling framework is demonstrated on a problem of a fluid flow in a contact interface between a solid with representative rough surface and a rigid flat. The evolution of the contact pressure, fluid flow pattern and the morphology of trapped fluid zones under increasing external load until the complete sealing of the interface is displayed. Finally, effective properties of flat-on-flat rough contact interfaces such as transmissivity and real contact area growth are calculated using the developed framework, showing qualitatively new results compared to the one-way coupling approximation. KeywordsFinite-element method • mechanical contact • thin fluid flow • trapped fluid • monolithic coupling