A model of adhesion coupled to contact and friction

An original law of adhesion is developed and coupled to the classical laws of unilateral contact and threshold friction. Its originality stems from the choice of an irreversible decohesion gap for internal variable, together with an adhesive tension for conjugate stress. Adhesion is modeled as a tension limit at zero gap and decohesion as a linear “plastic” softening over a finite gap, which makes the law more realistic than previous ones. The whole tribological law is formulated within the framework of standard generalized materials adapted to interfaces. For solution purposes, the law is next regularized using either the approximate penalty or the exact augmented Lagrangian method. The corresponding quasi-incremental minimisation and minimaximisation contact problems are formulated. The model is illustrated by the numerical simulations of the decohesion of a rigid parabolic punch on an elastic half-space and the pull-out of a fibre embeded in a matrix.