Abstract
Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or ‘spring-type’ interfacial conditions are not able to predict bifurcations in tension, while experiments—one of which, ad hoc designed, is reported—show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.
Highlights
Lubricated sliding along an interface between two deformable bodies is typically characterized by very low2018 The Authors
A distinctive feature of lubricated soft contacts is that they are capable of sustaining tensile contact tractions during sliding, in transient conditions, a phenomenon clearly visible when a suction cup is moved on a lubricated substrate
A ‘T-shaped’ silicon rubber element is clamped at the lower end and connected at the upper flat end to a silicon rubber suction cup, which has been applied with a lubricant oil
Summary
A bilateral and frictionless sliding contact condition has been often employed to model the above-mentioned problems (for instance, in geophysics [7], or for sliding inclusions [8], or rollbonding of metal sheets [9]), where two bodies in a current configuration share a common surface along which shear traction and normal separation/interpenetration must both vanish, but free sliding is permitted Another model is based on a ‘spring-like’ interface, in which the incremental nominal traction is related to the jump in the incremental displacement across the interface (see [10,11]). This model, in the limit of null tangential stiffness and null normal compliance should reduce to the sliding interface model While these models are elementary within an infinitesimal theory, they become complex when the bodies in contact suffer large displacement/strain (and may evidence bifurcations, as in the case of the soft materials involved in the experimental set-up shown in figure 1). So that, using equations (2.27), (2.28) and (2.15), the following expressions are derived:
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