A consistent model coupling adhesion, friction, and unilateral contact

Abstract

A model considering both unilateral contact, Coulomb friction, and adhesion is presented. In the framework of continuum thermodynamics, the contact zone is considered as a material boundary and the local constitutive laws are derived by choosing two specific surface potentials: the free energy and the dissipation potential. Because of the non-regular properties of these potentials, convex analysis is used to derive the local behavior laws from the state and the complementary laws. The adhesion is characterized by an internal variable β, introduced by Frémond, which represents the intensity of adhesion. The continuous transition from a total adhesive condition to a possible pure frictional one is enforced by using elasticity coupled with damage for the interface. Non-penetration conditions and Coulomb law are strictly imposed without using any penalty. The variational formulation for quasistatic problems is written as the coupling between an implicit variational inequality, a variational inequality, and a differential equation. An increment formulation is proposed. An existence result under a condition on the friction coefficient is given. A numerical method is derived from the incremental formulation and various algorithms are implemented: they solve a sequence of minimization problems under constraints. The model is used to simulate a micro-indentation experiment conducted to characterize the behavior of fiber/matrix interface in a ceramic composite. Identification of the constitutive parameters is discussed.