A deductive theory of friction

Abstract

The contact problem between two bodies is revisited, considering the existence of a third material body having a small thickness separating the two solids. The contact problem is now posed over a three-body system, with an intermediate layer-called interphase-which is imparted a specific constitutive law. Starting from a variational formulation problem set up over a three-dimensional domain, a perturbative method is used to derive a set of successive problems, depending on a small parameter. The first order problem describes the limit situation of an interphase having a vanishing thickness; higher order problems establish a correction of the first order solution with respect to the thickness variation. In this way, it is shown that general contact laws with or without friction can be deduced-instead of being postulated-and their forms depend in an essential way of the constitutive behaviour of the interphase. Particularly, one recovers Coulomb's friction law when the two solids are brought into contact through a thin fluid layer obeying Navier-Stokes equations. Finally, unilaterality is discussed in conjunction with the adhesion conditions between both solids. © 1995.