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A consistent model coupling adhesion, friction, and unilateral contact. (English) Zbl 0949.74008
Summary: We present a model considering unilateral contact, Coulomb friction, and adhesion. In the framework of continuum thermodynamics, the contact zone is treated 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 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 $$\beta$$ which represents the intensity of adhesion. The continuous transition from a total adhesive condition in 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. We propose an incremental formulation, and give an existence result under a condition on the friction coefficient. 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. Finally, we discuss the identification of constitutive parameters.

##### MSC:
 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74M10 Friction in solid mechanics 74A15 Thermodynamics in solid mechanics 74E30 Composite and mixture properties
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