An associated model of Coulomb friction based on the real area of contact

Abstract

Coulomb friction is a non-associated law: it contains a threshold that depends on the contact pressure, i.e. a stress that is not conjugate to any internal variable, hence it admits no dissipation potential in the sense of generalized standard materials (GSM), and the incremental frictional contact problem is not a minimization problem. In this paper, we propose an alternative friction model that retains Coulomb-like behavior while being associated and fully GSM-compatible. Key to our formulation is the introduction of a new internal variable motivated by the microscopic contact state of rough surfaces, whose evolution is driven by the plastic deformation of the asperities. Under a non-decreasing contact pressure and below a threshold pressure, the model recovers Coulomb friction up to an asperity-scale penetration depth. This depth is physically meaningful and can be calibrated to reproduce known tribology results. Under decreasing contact pressures, the model exhibits a memory effect due to irreversible plastic deformation of the asperities, whereas above the pressure threshold it yields a saturation of the frictional traction. We present both penalty and Lagrange multiplier formulations of the model. A 2D finite element implementation of the penalty approach confirms excellent agreement with the classical Coulomb predictions across two benchmark tests.