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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.

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
Full Text: DOI
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