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  1. Abstract

    Lubricated contacts in soft materials are common in various engineering and natural settings, such as tires, haptic applications, contact lenses, and the fabrication of soft electronic devices. Two major regimes are elasto‐hydrodynamic lubrication (EHL), in which solid surfaces are fully separated by a fluid film, and mixed lubrication (ML), in which there is partial solid‐to‐solid contact. The transition between these regimes governs the minimum sliding friction achievable and is thus very important. Generally, the transition from EHL to ML regimes is believed to occur when the thickness of the lubricant layer is comparable with the amplitude of surface roughness. Here, it is reported that in lubricated sliding experiments on smooth, soft, poly(dimethylsiloxane) substrates, the transition can occur when the thickness of the liquid layer is much larger than the height of the asperities. Direct visualization of the “contact” region shows that the transition corresponds to the formation of wave‐like surface wrinkles at the leading contact edge and associated instabilities at the trailing contact edge, which are believed to trigger the transition to the mixed regime. These results change the understanding of what governs the important EHL–ML transition in the lubricated sliding of soft solids.

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  2. An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically uses iteration techniques. A difficulty with iteration schemes is that convergence becomes increasingly difficult under increasingly heavy loads. Here we devise a numerical scheme that does not involve iteration. Instead, a linear problem is solved at every time step. The scheme is fully automatic, stable and efficient. We illustrate this technique by solving a relaxation test in which a rigid spherical indenter is brought rapidly into normal contact with a thick elastic substrate lubricated by a liquid film. The sphere is then fixed in position as the pressure relaxes. We also carried out relaxation experiments on a lubricated soft PDMS (polydimethysiloxane) substrate under different conditions. These experiments are in excellent agreement with the numerical solution. 
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    The interface between two surfaces patterned with complementary shapes such as arrays of ridge–channel structures or pillars accommodates relative misorientation and lattice mismatch by spontaneous production of dislocation arrays. Here, we show that the relative sliding of such an interface is accomplished by dislocation glide on the interfacial plane. An exception is the singular case where the lattices are perfectly matched across the sample dimension, in which case sliding is accompanied by motion of edge-nucleated defects. These are meso-scale analogues of molecular sliding friction mechanisms between crystalline interfaces. The dislocations, in addition to the long-range elastic energy associated with their Burgers vectors, also cause significant out-of-plane dilation, which props open the interface locally. For this reason, the sliding friction is strongly pressure dependent; it also depends on the relative orientation of the patterns. Sliding friction can be strongly enhanced compared with a control, showing that shape-complementary interfaces can be engineered for strongly enhanced pressure- and orientation-dependent frictional properties in soft solids. 
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  5. Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings. It very often occurs in the iso-viscous elasto-hydrodynamic lubrication (EHL) regime ( e.g. , soft solid, low pressure). In this regime, for sliding of a smooth sphere on a soft solid, a “Hertz-like” effective contact region forms. Much of the fluid is squeezed out of the contact region although enough is retained to keep the solid surfaces fully separated. This is accompanied by complex deformation of the soft solid. The behavior of such soft lubricated contacts is controlled by a single dimensionless parameter 1/ β that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large β , which is the limit relevant for soft solids. As a consequence, little is known about the structure of the flow field under soft lubrication in the intake and outlet regions. Here we present a new solution of this soft lubrication problem focusing on the “Hertz” limit. We develop a formulation in polar coordinates that handles difficult computational issues much better than previous methods. We study how hydrodynamic pressure, film thickness and hydrodynamic friction vary with β . Scaling laws for these relationships are given in closed form for a range of β not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems. 
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  6. Lubricated contacts are present in many engineering and biological systems involving soft solids. Typical mechanisms considered for controlling the sliding friction in such lubricated conditions involve bulk material compliance, fluid viscosity, viscoelastic response of the material (hysteretic friction), and breaking of the fluid film where dry contact occurs (adhesive friction). In this work we show that a two-phase periodic structure (TPPS), with a varying modulus across the sliding surface, provides significant enhancement of lubricated sliding friction when the system is in the elastohydrodynamic lubrication (EHL) regime. We propose that the enhanced friction is due to extra energy loss during periodic transitions of the sliding indenter between the compliant and stiff regions during which excess energy is dissipated through the fluid layer. This is a form of elastic hysteresis that provides a novel mechanism for friction enhancement in soft solids under lubricated conditions. 
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