We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for frictionless and frictional contact. Using this model we investigate the evolution of the real contact area, maximal frictional traction and global coefficient of friction under increasing external pressure. Elastic and elasto-plastic material models, compressible and incompressible fluid models and different geometrical characteristics of the wavy surface are used. We show that in case of incompressible fluid, due to its pressurization, the real contact area and the global coefficient of friction decrease monotonically with the increasing external pressure. Ultimately the contact opens and the fluid occupies the entire interface resulting in vanishing of static friction. In case of compressible fluids with pressure-dependent bulk modulus, we demonstrate a non-monotonous behaviour of the global coefficient of friction due to a competition between non-linear evolution of the contact area and of the fluid pressure. However, for realistic compressibility of solids and fluids, contact-opening cannot be reached at realistic pressures. An asymptotic analytical result for the trap-opening pressure is found and shown to be independent of the surface slope if it is small. On the other hand, in case of elasticperfectly plastic materials, we again observe fluid permeation into the contact interface. Finally, we study the distribution of frictional tractions during the depletion of the contact area under increasing pressure. This process leads to emergence of singularity-like peaks in the tangential tractions (bounded by the Coulomb's limit) near the contact edges. We point out the similarity between the processes of trap opening and interfacial crack propagation, and estimate the complex stress intensity factor in the framework of linear elastic fracture mechanics.

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A pressure driven flow in contact interface between elastic solids with wavy surfaces is studied. We consider a strong coupling between the solid and the fluid problems, which is relevant when the fluid pressure is comparable with the contact pressure. An approximate analytical solution is obtained for this coupled problem. A finite-element monolithically coupled framework is used to solve the problem numerically. A good agreement is obtained between the two solutions within the region of the validity of the analytical one. A powerlaw interface transmissivity decay is observed near the percolation. Finally, we showed that the external pressure needed to seal the channel is an affine function of the inlet pressure and does not depend on the outlet pressure.

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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

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